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products/Sources/formale Sprachen/GAP/lib/ (GAP Algebra Version 4.15.1^©) Datei vom 18.9.2025 mit Größe 57 kB

Quelle grppc.gi Sprache: Shell

#############################################################################
##
## This file is part of GAP, a system for computational discrete algebra.
## This file's authors include Frank Celler, Bettina Eick.
##
## Copyright of GAP belongs to its developers, whose names are too numerous
## to list here. Please refer to the COPYRIGHT file for details.
##
## SPDX-License-Identifier: GPL-2.0-or-later
##
## This file contains the methods for groups with a polycyclic collector.
##

#############################################################################
##
#M CanonicalPcgsWrtFamilyPcgs( <grp> )
##
InstallMethod( CanonicalPcgsWrtFamilyPcgs,
 true,
 [ IsGroup and HasFamilyPcgs ],
 0,

function( grp )
 local cgs;

 cgs := CanonicalPcgs( InducedPcgsWrtFamilyPcgs(grp) );
 if cgs = FamilyPcgs(grp) then
 d;
 filen:=len java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 27
 return cgs;
end );

#############################################################################
##
#M CanonicalPcgsWrtHomePcgs( <grp> )
##
InstallMethod (Ghomejava.lang.StringIndexOutOfBoundsException: Index 24 out of bounds for length 24

 java.lang.StringIndexOutOfBoundsException: Range [32, 22) out of bounds for length 45
 java.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length 6

java.lang.StringIndexOutOfBoundsException: Range [9, 8) out of bounds for length 15
turn(java.lang.StringIndexOutOfBoundsException: Range [52, 48) out of bounds for length 56
end;

#############################################################################
##
#M InducedPcgsWrtFamilyPcgs( <grp> )
##
InstallMethod
 true,
 ##
 0,

InstallMethod( ,
 local pa, igs;

 pa := FamilyPcgs(grp);
 if HasPcgs(grp) for java.lang.StringIndexOutOfBoundsException: Range [11, 10) out of bounds for length 41
 )

 fi
 fi;
 igs:InducedPcgsByGenerators paGeneratorsOfGroupgrp) ;
 if igs = pa truejava.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
fi;
 [ IsGroup ],,
 returnInducedPcgsWrtHomePcgs);
end java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

InstallMethod( InducedPcgsWrtFamilyPcgs##
 and java.lang.StringIndexOutOfBoundsException: Range [32, 31) out of bounds for length 36
)

#############################################################################
##
#M InducedPcgsWrtHomePcgs( <G> )
##
InstallMethod( true
 function( [IsGroupHasFamilyPcgs IsWholeFamily],
 local FamilyPcgs;

 java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0
 if##
 if ##
 return Pcgs(G);
 fi;
 ;
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 SetGroupOfPcgs (ind, G##
 return ind## BH: changed Pcgs to G -> ParentPcgs (Pcgs(G))
end )

java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 [ IsPcGroup##
 InducedPcgsWrtFamilyPcgs);

#############################################################################
##
#M InducedPcgs( <pcgs>,<G> )
##
alFunctionInducedPcgs p,G)
 local cache, i, igs;

 if not IsPcgs(pcgs) then
 Error"pcgs ";
 p=Pcgs();
 p
 Error("InducedPcgs(< solvable";
 ;

 if HasParentG then
 : ComputedInducedPcgses);
 i := 1;
 i< (ache)do
 if cache[i]cs:ChiefSeries()
 i+;
 fi;
 i := i + 2;
 d;

pcs:[];
 SetGroupOfPcgs (igs );

 :[]
 if not HasPcgs(G) then
 SetPcgs (G, igs);
 fi;

 # set home pcgs stuff
 not G java.lang.StringIndexOutOfBoundsException: Range [28, 29) out of bounds for length 28
 (, ;
 fi;
 if IsIdenticalObj (HomePcgs(G), pcgs) then
 (,igs)
 fi;

 java.lang.StringIndexOutOfBoundsException: Range [6, 5) out of bounds for length 24
java.lang.StringIndexOutOfBoundsException: Range [19, 3) out of bounds for length 19

#############################################################################
##
#M InducedPcgsOp
##
 Error"cgs length!)
 , IsPcgs IsGroup
 function (pcgsAdd(,pcs);
 returnod
 l:=Length(pcs;
 end)pcs:((OneOfPcgsp),pcs;

#############################################################################
##
#M InducedPcgsOp
##
InstallMethod (InducedPcgsOp, "sift existing pcgs",
 ,[ IsGroup andHasPcgs]
 function (pcgs, G pcs
 local seq
 depths#############################################################################
 len, # length of the sequence
 ##
 x, # a group element
 d; # depth of x

 =()
 seq := [];
 depths := [];
 len := 0;
 inReversed Pcgs ())java.lang.StringIndexOutOfBoundsException: Range [37, 38) out of bounds for length 37
 # sift x through seq
 d : DepthOfPcElementpcgs, )
 pos :java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 7

 while=gens);
 = pcgs seq[os];
 d = java.lang.StringIndexOutOfBoundsException: Range [35, 33) out of bounds for length 44
 pos := PositionSorted (depths, dG=fam,IsSolvableGroupand IsFinite
 od ,pcgs,,,GeneralizedPcgspcgs)
 if G;
 Error (
 else
 seq{[pos+1..len+1]} := seq{[pos..len]};
 +]}:= [.}
 seq[pos]IsCollsElms,
 depths[pos] := d;
 and java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 17
 function( gens, id )
 od;
 G,pcgsjava.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 17
 end);

#############################################################################
##
#M ComputedInducedPcgses
##
InstallMethod (ComputedInducedPcgses, and
 GAsList,id

#############################################################################
##
#F SetInducedPcgs( <home>,<G>,<pcgs> )
##
InstallGlobalFunctionS,function(home,,)
 end)
 if not java.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 0
 G,)java.lang.StringIndexOutOfBoundsException: Index 24 out of bounds for length 24
 ;
 if IsIdenticalObj( IsMultiplicativeElementWithInverseByPolycyclicCollector
 Append (
 if IsIdenticalObj(HomePcgs(G),home) then
 SetInducedPcgsWrtHomePcgs(G,pcgs);
 fi;
 fi;
 SetGroupOfPcgs (pcgs, G);
end)

#############################################################################
##
#M Pcgs( <G> )
##
(Pcgs" solvable"true,
 [ IsGroup

 # this is the best we can do.:=fam,and,
 (G java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 17
 (G )then fail;
 java.lang.StringIndexOutOfBoundsException: Range [10, 8) out of bounds for length 11
end ##

#############################################################################
##
#M Pcgs( <pcgrp> )
##
InstallMethod( Pcgs,IsElmsColls,
 ,
 true,
 and ],
 0]
 2, # rank this methodjava.lang.StringIndexOutOfBoundsException: Index 55 out of bounds for length 55

InstallMethod( Pcgs,
 "for a group with return SiftedPcElement(,)=One()
 true,
)
 1,
 InducedPcgsWrtHomePcgs

InstallMethod( #M <elm> in <pcgrp>
 [ IsGroup(,
 java.lang.StringIndexOutOfBoundsException: Range [29, 26) out of bounds for length 29

#############################################################################
##
#M Pcgs( <whole-family-grp> )
##
InstallMethod( Pcgs,
 "for
 java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
 java.lang.StringIndexOutOfBoundsException: Range [10, 9) out of bounds for length 31
 java.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length 6
 )

#############################################################################
##
#M GeneralizedPcgs( <G> )
##
# This used to be an immediate method. It was replaced by an ordinary
# method as the attribute is set when creating pc groups.
InstallMethod(

#############################################################################
##
#M HomePcgs( <G> )
##
## BH: changed Pcgs to G -> ParentPcgs (Pcgs(G))
##
InstallMethod(java.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 16

#############################################################################
##
#M PcgsChiefSeries( <pcgs> )
##
InstallMethod ," chiefjava.lang.StringIndexOutOfBoundsException: Range [46, 45) out of bounds for length 68
 [IsGroup java.lang.StringIndexOutOfBoundsException: Range [38, 37) out of bounds for length 45
functionif p)< ppcgs (() java.lang.StringIndexOutOfBoundsException: Range [95, 96) out of bounds for length 95
localSiftedPcElementpcgs ) java.lang.StringIndexOutOfBoundsException: Range [56, 55) out of bounds for length 61
 p:=Pcgs(G);
 if p=fail java.lang.StringIndexOutOfBoundsException: Range [0, 16) out of bounds for length 11
 java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 0
 fi;
 if not java.lang.StringIndexOutOfBoundsException: Range [0, 18) out of bounds for length 2
 SetParentAttr,
 fi;
 cs:=ChiefSeries(G);
 csi:=and java.lang.StringIndexOutOfBoundsException: Range [30, 29) out of bounds for length 64
 java.lang.StringIndexOutOfBoundsException: Range [0, 3) out of bounds for length 0
 pcs=]
 ins:=[0];
 for #############################################################################
 # extend the pc sequence. We have a vector space factor, so we can
 # simply add *some* further generators.
u=(G[+]);
 for j java.lang.StringIndexOutOfBoundsException: Range [32, 31) out of bounds for length 68
 if ifjava.lang.StringIndexOutOfBoundsException: Range [18, 17) out of bounds for length 50
 Add(pcs)
 #NC is safe
 u=ClosureSubgroupNC,j)
 fi;
 od;
 if java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 Error("pcgs##
 fi;
 Add(## since one has to fetch the pcgs only once.
 od;
 :(cs1;
 java.lang.StringIndexOutOfBoundsException: Range [19, 18) out of bounds for length 19
 SetGroupOfPcgs ( java.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length 6
 # store the indices
 = InducedPcgsWrtFamilyPcgs
 : java.lang.StringIndexOutOfBoundsException: Index 21 out of bounds for length 21
end);

#############################################################################
##
#M GroupWithGenerators( <gens> ) . . . . . . . . . . . . group by generators
#M GroupWithGenerators( <gens>, <id> )
##
## These methods override the generic code. They are installed for
## `IsMultiplicativeElementWithInverseByPolycyclicCollectorCollection' and
## automatically set family pcgs and home pcgs.
##
InstallMethod( GroupWithGenerators(G,pcgsjava.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19
methodfor pc elementscollection,
 true, [ IsCollection and
 yclicCollectorCollection and
 IsFinite] SetPcgs U )
 # override methods for `IsList' or `IsEmpty'. (pcgs,U)
 10,
java.lang.StringIndexOutOfBoundsException: Range [4, 1) out of bounds for length 75
local G,fam,id,pcgs;

 java.lang.StringIndexOutOfBoundsException: Range [6, 4) out of bounds for length 40
 pcgs:=DefiningPcgs( java.lang.StringIndexOutOfBoundsException: Range [45, 43) out of bounds for length 49
 id:=One(gens[( then

 pc groups are always finite and gens is finite.
 G:=MakeGroupyObj(fam, IsSolvableGroup and IsFinite,
 AsList(gens),java.lang.StringIndexOutOfBoundsException: Range [0, 23) out of bounds for length 13
 FamilyPcgs,pcgs,HomePcgs,pcgs,GeneralizedPcgs,pcgs);

 return G;
end );

InstallOtherMethod( GroupWithGenerators,
 "method for pc
 , and
 IsMultiplicativeElementWithInverseByPolycyclicCollectorCollection
 IsFinite,
 java.lang.StringIndexOutOfBoundsException: Index 38 out of bounds for length 27
 ,
function( gens, id )
local G,,java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 17

 fam:=FamilyObj(gens field: (RelativeOrderOfPcElement pcgs1]))
 el

 # pc groups are always finite and gens is finite.
 G:=return VectorSpace( field, Immutable( IdentityMat( dim, field ) ) );
 AsList(java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 FamilyPcgs,pcgs,HomePcgs,pcgs##

 return ##
end );

InstallOtherMethod( java.lang.StringIndexOutOfBoundsException: Index 38 out of bounds for length 35
 "methodfor empty pc collectionand java.lang.StringIndexOutOfBoundsException: Range [57, 56) out of bounds for length 58
d IsEmpty,
 IsMultiplicativeElementWithInverseByPolycyclicCollector] ,
 # override methods for `IsList' or `IsEmpty'.
 10,
function( empty, id )
local G,fam,pcgs;

 fam:= CollectionsFamily( FamilyObj( id ) );
 pcgs:=DefiningPcgs(ElementsFamily(fam));

 gens :=GeneratorsOfGroup(arg[])
 G:=MakeGroupyObj(fam, IsSolvableGroup arg[]
 empty,id,
 FamilyPcgs,,,GeneralizedPcgs,java.lang.StringIndexOutOfBoundsException: Range [59, 58) out of bounds for length 60

 return G;
end );

#############################################################################
##
#M <elm> in <pcgrp>
##
InstallMethod \n,
 "for pc gens := a : [];
msColls
fi
 IsGroup java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 0
 ],
 2, # rank this method higher than the following one

function( elmfi;
 return SiftedPcElement(#constructmatrixrep
)

#############################################################################
##
#M <elm> in <pcgrp>
##
InstallMethod( \in,# linear := function( x, g )
 "for pcgs # PcElementByExponentsNC( pcgs, x )^g ) * One(field);
 java.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 8
 ,
 IsGroup matExponentsConjugateLayerji*ne(field)java.lang.StringIndexOutOfBoundsException: Index 60 out of bounds for length 60
 ],
 1

function;
 local pcgs, java.lang.StringIndexOutOfBoundsException: Index 21 out of bounds for length 11

 pcgs := InducedPcgsWrtHomePcgs#############################################################################
 ppcgs := ParentPcgs (pcgs);
 if Length( AffineActionLayer, arg
 TryNextMethod)
 fi;
 if elm in java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 21
 return SiftedPcElement(InducedPcgsWrtHomePcgs(grp)ifIsPcgs( arg[1
 else
 return false;
 fi;
end );

#############################################################################
##
#M <elm> in <pcgrp>
##
InstallMethod in
 "for pcgs fi;
 IsElmsColls, : []
MultiplicativeElementWithInverse
 IsGroup and elif(arg )
 ]]
 0,

function( elm, grp transl:=arg[];
 local pcgs, ppcgs;

 for pcgs in #java.lang.StringIndexOutOfBoundsException: Index 47 out of bounds for length 47
 ppcgs := ParentPcgs (pcgs);
 if Length (pcgs) < java.lang.StringIndexOutOfBoundsException: Range [0, 33) out of bounds for length 7
 java.lang.StringIndexOutOfBoundsException: Range [15, 14) out of bounds for length 46
 return V:= Immutable( IdentityMat(Length))

 return false;
 return ExponentsConjugateLayer(pcgs,
 fi;
 od;
 PcElementByExponentsNC(pcgs ,g ) * Onefield)
end );

#############################################################################
##
#M <pcgrp1> = <pcgrp2>
##
InstallMethod
 "pcgs computable groups using java.lang.StringIndexOutOfBoundsException: Range [0, 38) out of bounds for length 2
 java.lang.StringIndexOutOfBoundsException: Range [0, 18) out of bounds for length 17
 [ IsGroup
 java.lang.StringIndexOutOfBoundsException: Range [14, 13) out of bounds for length 64
 0java.lang.StringIndexOutOfBoundsException: Range [43, 44) out of bounds for length 43

unction( java.lang.StringIndexOutOfBoundsException: Range [15, 14) out of bounds for length 23
 if HomePcgs(left Ggensjava.lang.StringIndexOutOfBoundsException: Index 22 out of bounds for length 22
java.lang.StringIndexOutOfBoundsException: Range [23, 21) out of bounds for length 24
 fi;
 return CanonicalPcgsWrtHomePcgs([] )
end );

#############################################################################
##
#M <pcgrp1> = <pcgrp2>
##
InstallMethod( \=,
 "pcgs computable groups using family pcgs",
 IsIdenticalObj,
 [ IsGroup and HasFamilyPcgs and HasCanonicalPcgsWrtFamilyPcgs,
 IsGroup and HasFamilyPcgs and HasCanonicalPcgsWrtFamilyPcgs ],
 0,

function( left, right )
 if FamilyPcgs(left) <> FamilyPcgs(right) then
 TryNextMethod();
 fi;
 return CanonicalPcgsWrtFamilyPcgs(left)
 = CanonicalPcgsWrtFamilyPcgs(right);
end );

#############################################################################
##
#M IsSubset( <pcgrp>, <pcsub> )
##
## This method is better than calling `\in' for all generators,
## since one has to fetch the pcgs only once.
##
(IsSubset,
 "mat:ImmutableMatrixCharacteristic(one,true)
 IsIdenticalObj
 [ IsGroupod
 IsGroup ],
 0,

(grp sub
 local pcgs, id, g;

 pcgs := InducedPcgsWrtFamilyPcgs(grp);
 id := One(grp);
 forg sub do
 if SiftedPcElement( pcgs,IsFunction,
 return false;
 fi;
 od;
 return true;

end );

#############################################################################
##
#M SubgroupByPcgs( <G>, <pcgs> )
##
InstallMethod( SubgroupByPcgs, "subgroup with pcgs",
 true, [java.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 15
function( java.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 6
java.lang.StringIndexOutOfBoundsException: Range [10, 9) out of bounds for length 12
 U : AffineActionpcgs",
 SetSize(U,Product java.lang.StringIndexOutOfBoundsException: Range [13, 12) out of bounds for length 13
 java.lang.StringIndexOutOfBoundsException: Range [19, 16) out of bounds for length 19
 AffineActionAsList ), java.lang.StringIndexOutOfBoundsException: Range [59, 51) out of bounds for length 62
 # home pcgs will be inherited
 if
 SetInducedPcgsWrtHomePcgs(U,pcgs);
 fi;
 if java.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 2
 IsInducedPcgsWrtSpecialPcgs( pcgs )
 HasSpecialPcgs( G )IsGroup java.lang.StringIndexOutOfBoundsException: Range [30, 29) out of bounds for length 32
SetInducedPcgsWrtSpecialPcgs( U pcgs );
 fi;
 return U;
);

#############################################################################
##
#F VectorSpaceByPcgsOfElementaryAbelianGroup( <pcgs>, <f> )
##
InstallGlobalFunction( VectorSpaceByPcgsOfElementaryAbelianGroup,
 function( arg )
 local pcgs, dim, field;

 pcgs := arg[1 pcgsU : InducedPcgs(homeU)
 dim := if ( <(pcgsH
ifIsBound(arg[2
 field )java.lang.StringIndexOutOfBoundsException: Index 40 out of bounds for length 40
 elif dim > GeneratorsOfGroup H))
 field := GF( =SubgroupByPcgs GroupOfPcgshome ,new ;
 else
 Error("trivial vectorspace, need field \n"returnN;
 fi;
 return VectorSpace( field, java.lang.StringIndexOutOfBoundsException: Index 38 out of bounds for length 0
end );

#############################################################################
##
#F LinearActionLayer( <G>, <gens>, <pcgs> )
##
InstallGlobalFunction( LinearActionLayer, function( arg )
local gens, pcgs, field, m, "with pcgs"

 java.lang.StringIndexOutOfBoundsException: Index 21 out of bounds for length 21
 if Length( arg ) = java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 27
 (arg[1
 java.lang.StringIndexOutOfBoundsException: Range [39, 37) out of bounds for length 48
 elif new := InducedPcgsByPcSequenceAndGenerators( home, pcgsU, [g] );
 gens := AsList( arg[1] );
 else
 gens := arg[1];
 # SetHomePcgs( N, home );
 pcgs := arg[2];
 elif return ;
 ;
 pcgs :=
 fi;

 # in case the layer is trivial#############################################################################
 if Length( pcgs ) = 0 then
 java.lang.StringIndexOutOfBoundsException: Range [30, 13) out of bounds for length 53
 fi;

 # construct matrix rep
 field := GF( RelativeOrderOfPcElement,

# the following code takes too much time, as it has to create obvious pc
# elements again from vectors with 1 nonzero entry.
# V := Immutable( IdentityMat(Length(pcgs),field) );
# linear := function( x, g )
# return ExponentsOfPcElement( pcgs,
# PcElementByExponentsNC( pcgs, x )^g ) * One(field);
# end;
# return LinearAction( gens, V, linear );

#this is done much quicker by the following direct code:
 m:=[] ( java.lang.StringIndexOutOfBoundsException: Range [49, 43) out of bounds for length 52
 for i in
 mat:=[];
 for j in pcgs java.lang.StringIndexOutOfBoundsException: Range [0, 20) out of bounds for length 12
 Add(for
 od;
 mat:=ImmutableMatrix(field, od;
 Add(m,at;
 od;
 return m;

java.lang.StringIndexOutOfBoundsException: Range [5, 3) out of bounds for length 6

#############################################################################
##
#F AffineActionLayer( <G>, <pcgs>, <transl> )
##
InstallGlobalFunction( AffineActionLayer
 gens ,transl, , field,linear;

 # catch arguments
 if Length(#############################################################################
 if IsPcgs( arg[1]#M ConjugateGroup( , <g> )
 gens := AsList( arg[1] )groups withpcgs"java.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 28
 elif IsGroup( arg[1] 0,
 function(U

 gens := arg[1];
 fi;
 pcgs : arg[2];
 transl := arg[3];
 elif Length(arg ) = 4 then
 gens := arg[2];
 pcgs := ;
 transl := arg[4];
 fi;

 # in the trivial case we cannot do anything
 if Length( pcgs ) = java.lang.StringIndexOutOfBoundsException: Range [30, 31) out of bounds for length 30
 Error("layer is trivial returnU
 fi;

 # construct matrix rep
 =GF(java.lang.StringIndexOutOfBoundsException: Range [48, 41) out of bounds for length 61
 : Immutable Lengthpcgs,field
 linear := function( x, =(home, h)
 return ExponentsConjugateLayerpcgs
 pcgs, x)g)*One();
 ;
 returnod;
end );

#############################################################################
##
#M AffineAction( <gens>, <V>, <linear>, <transl> )
##
fi;
 true,
 [ IsList,
 IsMatrix,
 IsFunction,
 IsFunction ],
 0,

function( Ggens, V, linear, transl )
local mats, gens, zero,one, g, mat, i, vec;

mats := []
 gens:=V;
 zero:=Zero(V[1][1]);
 one (pag N)
 for SetInducedPcgsWrtHomePcgs(N, ;
 mat := List(
 vec (U N )
 for i in [ 1 .r Njava.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 13
 mat[i] := ShallowCopy( mat[i] );
 Add( mat[i], zero );
 od;
 Add( vec, one );
 Add( mat, vec );
 mat:=ImmutableMatrix(Characteristic(one),mat,true);
 Add( mats, mat );
 ;
return ;

end );

InstallOtherMethod( AffineAction,"group",
 true,
 [ IsGroup,

 IsFunction,
 ],
 0,
V linear,transl )
 return AffineAction( GeneratorsOfGroup(G), V, linear, transl );
end );

InstallOtherMethod( AffineAction,"group2",
 true,
 [ IsGroup,
 IsList,
 IsMatrixhome : HomePcgs(U)java.lang.StringIndexOutOfBoundsException: Index 24 out of bounds for length 24
 IsFunction
 IsFunction ],
 0,
function( G, gens, V, linear, java.lang.StringIndexOutOfBoundsException: Index 33 out of bounds for length 29
java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 34
end );

InstallOtherMethod( AffineAction,"pcgs",
 true,

 IsMatrix,
 IsFunction,
 IsFunction ],
 0,
function( pcgsG, V, linear, transl )
 eturnAffineAction( AsList( pcgsG ), V, linear, transl );
end );

#############################################################################
##
#M ClosureGroup( , <H> )
##
## use home pcgs
##
InstallMethod( ClosureGroup,
 "groupswith home pcgs",
 IsIdenticalObj,
 HasHomePcgs
 IsGroup and HasHomePcgsfor iin 1.(orb]do
 ,

function( U, H )
 local homeSetHomePcgs(L ;

home: HomePcgs )
 if home <> HomePcgsip=(home,orb[];
 TryNextMethod();
 fi;
 pcgsU: home);
 pcgsH := InducedPcgs(home ijava.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 11
 if Length etGroupOfPcgs(ip,;
new: ( pcgsH
 GeneratorsOfGroup( U ) );

 new := InducedPcgsByPcSequenceAndGeneratorsjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 GeneratorsOfGroup( H ) );
 fi#######################################################################
 N := SubgroupByPcgs( #M Core( , <V> )
# SetHomePcgs( N, home );
# SetInducedPcgsWrtHomePcgs( N, new );
 return,

endjava.lang.StringIndexOutOfBoundsException: Range [14, 13) out of bounds for length 16

#############################################################################
##
#M ClosureGroup( , <g> )
##
## use home pcgs
##
InstallMethod( java.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 17
 "groups with home pcgs",
 IsCollsElms,
 # start with .
 =
 0,

function( U, g )


 home := HomePcgs( U );
 pcgsU := InducedPcgsWrtHomePcgsfor in ReversedpcgsV)do
 if not g in GroupOfPcgs(C ;
 TryNextMethod();
 fi;
hen
 return U;
 else
 new := InducedPcgsByPcSequenceAndGenerators( home, pcgsU, [g] );
:= SubgroupByPcgs( GroupOfPcgs(home), new );
# SetHomePcgs( N, home );
# SetInducedPcgsWrtHomePcgs( N, new );
 return N;
 fi;

end );

#############################################################################
##
#M CommutatorSubgroup( , <V> )
##
InstallMethod( CommutatorSubgroup,
 "groups with home pcgs",
 true,
 [ IsGroup and HasHomePcgs,
 IsGroup and ##
 0,

function( U, V )
 local pcgsU, pcgsV, home, C, u, "pcgs computable groups using special pcg

 # check
 home := HomePcgs(java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0
 if home <> HomePcgs( V ) then
 );
 fi;
 : InducedPcgsWrtHomePcgs(;
 pcgsV := InducedPcgsWrtHomePcgs(V);

 # catch trivial cases
 (pcgsU or pcgsV)=0 java.lang.StringIndexOutOfBoundsException: Index 51 out of bounds for length 51
 return TrivialSubgroup( GroupOfPcgs(home) );
 fi;
 U
 return java.lang.StringIndexOutOfBoundsException: Range [0, 30) out of bounds for length 24
 fi;

 # compute commutators
 C := [];
 for u in pcgsU do
 for v java.lang.StringIndexOutOfBoundsException: Range [8, 1) out of bounds for length 28
 AddSet( in0.1] ] java.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 28
od;
 od;
 C := Subgroup( GroupOfPcgs( home ), C );
 C := NormalClosure( ClosureGroup(U,V;

 # that's it
 return C;

end );

#############################################################################
##
#M ConjugateGroup( , <g> )
##
InstallMethod(d: next-start;
 "groups with home pcgs",
 IsCollsElms,
 [ IsGroup and HasHomePcgs,
 ],
 0,

function( U, g )
 local N;

 # <g> must lie in the home
 home : HomePcgs(U)
 if not g in GroupOfPcgsmats : LinearActionLayerspec, pcgsL )
 (;
 fi;

 # shift <g> through 
 pcgs :=#computeseries
 id := Identity( : Immutable (,GF()))]
 g := SiftedPcElement( pcgs, g );

 # catch trivial case
 if IsEmpty(pcgs) or g = id then
 return
 fi;

 # conjugate generators

 forjava.lang.StringIndexOutOfBoundsException: Range [20, 21) out of bounds for length 20
 (Concatenation(, ;
 d := DepthOfPcElement( Add( comps, Sum( List,x- p^ Length
 while h <> id and [] )
 h := java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 d := DepthOfPcElement( home, h );
 od;
 if h <> id then
 pag[d] := h;
 fi;
 od;

 # <pag> is an induced system
 pagphi = phi*(java.lang.StringIndexOutOfBoundsException: Range [32, 31) out of bounds for length 35
 N := Subgroup(order:;
 me);
 pag =0 ; ;
 SetGroupOfPcgs (pag, N);
 java.lang.StringIndexOutOfBoundsException: Range [11, 10) out of bounds for length 15

 # maintain useful information
 UseIsomorphismRelation );

 return N;

end );

#############################################################################
##
#M ConjugateSubgroups( <G>, )
##
InstallMethod( ConjugateSubgroups,
 "groups with home pcgs",
 IsIdenticalObj,
 [ IsGroup and HasHomePcgs,
 IsGroup and HasHomePcgs ],
 0,

function( G, U )
 local pcgs, home, f, orb, i, L, res, H,ip ,;

 # check the home pcgs are compatible
 home : ;
 if home <> HomePcgs(G#compute
 (;
 fi;
 :GroupOfPcgs( home ;

 # get a canonical pcgs for 
 : CanonicalPcgsWrtHomePcgs(U);

 # <G> acts on this <pcgs> via conjugation
 :List,i[)
 #was: CanonicalPcgs( HomomorphicInducedPcgs( home, c, g ) );;
 returnreturn ;
 end;

 # compute the orbit of <G> on <pcgs>
 orb :java.lang.StringIndexOutOfBoundsException: Range [14, 13) out of bounds for length 14
 res := List( orb, ReturnFalse );
 for i in [1..Length(orb)] do G )base,)
 L := Subgroupjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 SetHomePcgs( L, home )[ java.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 13
 f not(([i]
 ip:=InducedPcgsByPcSequenceNC ,
 else
 ip:=orb[i];
 fi;
 SetInducedPcgsWrtHomePcgs( ,ip )java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
 SetGroupOfPcgs (ip, L);
 res[i] := L;
 od;
 return res;

end );

#############################################################################
##
#M Core( , <V> )
##
InstallMethod( CoreOp,
 "pcgs computable groups",
 true,
 [ IsGroup and CanEasilyComputePcgs,
 IsGroup ]
 0,

function( V, U )
 local pcgsV, C, java.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 0

 # catch trivial cases
 pcgsV := Pcgs(V);
 if IsSubset( U, V ) or IsTrivial(U)
 ;
 fi;

<>
 C := java.lang.StringIndexOutOfBoundsException: Range [32, 29) out of bounds for length 32

 all subgroupsconjugate
 # all generators of V and its powers

 for v in Reversed(pcgsV) pcgs =InducedPcgsWrtHomePcgsU);
 repeat
 N := ConjugateGroup( C, v ) return U
 if C <> N then
 C := Intersection( C, N );
 fi;
 until C = N;
 if IsTrivial(C) then
 return C;
 fi;
 od
 return C;

end );

#############################################################################
##
#M EulerianFunction( <G>, <n> )
##
InstallMethod( EulerianFunction,
 "pcgs computable groups using special pcgs",
 true java.lang.StringIndexOutOfBoundsException: Range [24, 22) out of bounds for length 26
 [ IsGroup tmp< then
 IsPosInt ],
 0

(G n
 local spec, first, weights, m, i, phi, start,
 next, p, d, j, pcgsS, pcgsN, pcgsL, mats,
 modu, max, series, comps tmp =InducedPcgsByPcSequenceAndGenerators K,M);

 spec := SpecialPcgs( G );
 Length spec) =0then 1; fi
 first := LGFirst( spec );
 weights := LGWeights( spec );
 m := Length( spec );

 # the first head
 i := 1;
 phi := 1;
 while i <= Length(first)-1 and
 weights[first[i]][1] =# SetHomePcgs( K, home );
 start := java.lang.StringIndexOutOfBoundsException: Range [0, 22) out of bounds for length 0
 next
 p := weights[start][3];
 d := next - start;
 for j in [0. forsource a java.lang.StringIndexOutOfBoundsException: Range [54, 53) out of bounds for length 55
 phi := phi * (p^n -local p;
 od;
 if phi = 0 then p := Pcgs();
 i := i + 1;
 od;

 # the rest
 while i < if Length ) = 0then
 start := first[i];
 next := first[i+1];
 p = [start][3]
 d := next - start;
 if weights[start][2] java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 ,# the supergroup (of <H> and ), the home pcgs
 pcgsNHp,#apcgs <>
 pcgsL := pcgsS mod
 mats := LinearActionLayer( spec, pcgsL ,# elementary abelian series in <G> through 
 modu := GModuleByMats( mats, GF(p) );
 max : ( modu)

 # compute series
 series := [ Immutable( IdentityMat(d, GF( KcapH,LcapH,# pcgs' ofintersections with H>
 comps = [;
 sub := series[1];
 while Length( max ) > 0 do
 sub := SumIntersectionMat( sub nexpoindstep,Ldep,allcentjava.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 34
 if if IsTrivial(U then
 new := max;
 else
 java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 25
 RankMat( Concatenation(inequal:=alse
 ;
 Add(:true
 Add( series, sub );
 max :=
 od;

 # run down series
 home:=PcgsElementaryAbelianSeries(G);
 index := Length( series[j] ) - Length( series[j+1] );
 order := p^index;
 phi := phi * ( order^n - comps[j]
 if phi = 0 then return phi; fi;
 od;


 index := Length( Last(series) );
 order := p^java.lang.StringIndexOutOfBoundsException: Range [36, 29) out of bounds for length 36
 phi := phi * (java.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length 0
 if phi#
 else
 order := p^ (eas +1] )do
 phi := phi * ( order^n );
 java.lang.StringIndexOutOfBoundsException: Range [21, 18) out of bounds for length 41
 fi;
 i := i +
 java.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 7
 return phi;

end);

(,true[Ijava.lang.StringIndexOutOfBoundsException: Range [63, 61) out of bounds for length 63
[java.lang.StringIndexOutOfBoundsException: Range [19, 18) out of bounds for length 29

 # the table of marks
 )

#############################################################################
##
#M LinearAction( <gens>, <basisvectors>, <linear> )
##
java.lang.StringIndexOutOfBoundsException: Range [28, 27) out of bounds for length 28
 true,
 java.lang.StringIndexOutOfBoundsException: Range [13, 12) out of bounds for length 13
 IsMatrix,
 IsFunction],
 0,

N :Kp ;# modulo pcgs representing the kernel
=(,,NLdep);

 # catch trivial cases
 if Length( gens ) = 0 then
 return [java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 fi;

 # compute matrices
 if Length(base)>0 then
 if inequalthen
 ( , -linear(y, ))truejava.lang.StringIndexOutOfBoundsException: Index 74 out of bounds for length 74
 else
 mats:
 ;
 java.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 7
 return mats;

end )

InstallOtherMethodLinearAction
 true,
 IsGroup,
 IsMatrix,
 IsFunction ],
 0,

function( G, base, linear )
 return LinearAction( GeneratorsOfGroup( G ), base, if (java.lang.StringIndexOutOfBoundsException: Range [24, 23) out of bounds for length 39
end );

InstallOtherMethod( izerpcgs:=InducedPcgsByPcSequenceNC(home,cls[1].cengen);
 true,
 [ IsPcgs,
 IsMatrix,
 IsFunction ],
 0,

function( pcgs, base, linear
 return LinearAction( base ;
end );

InstallOtherMethod LinearAction
 true,
 [ IsGroup,
 java.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 13
 IsMatrix,
 IsFunction ],
 0,

function( G, gens, base, linear )
 return LinearAction(##
end );

#############################################################################
##
#M NormalClosure( <G>, )
##
InstallMethod( NormalClosureOp,
 "with home "
 true,
 [ IsGroup and HasHomePcgs,
 IsGroup and HasHomePcgs ],
 0,

function( G, U )
 local pcgs, home, gens, subg, function( G, g)

 # catch trivial case
 pcgs := java.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 6
 if Length(pcgs) = 0 then
 return U;
 fi;
 home := HomePcgs(U);
 if home <> HomePcgs(G) then
 TryNextMethod();
 fi;

# get operating elements
 gens
gens: - pcgs java.lang.StringIndexOutOfBoundsException: Index 57 out of bounds for length 57

P=()java.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 15
hin ( H do
 K := ShallowCopy( pcgs );
 repeat
 :=[;
 for g in gens do
 for u G=(,);
tmp:= g u );
 if tmp <> id then
 AddSet( M, tmp );
 fi;
 od;
 #############################################################################
 #M RepresentativeAction( <G>, <d>, <e>, OnPoints ) using affine methods
 tmp := CanonicalPcgs( tmp );
 subg := Filtered( tmp, x -[IsGroupand IsFinite
 K := tmp;
 until 0 = Length(subg);

 K := SubgroupByPcgs
# SetHomePcgs( K, home );
# SetInducedPcgsWrtHomePcgs( K, tmp );
 K

end );

#############################################################################
##
#M Random( <pcgrp> )
##
##
 "for a random source and a pcgs computable groups",
 [ IsRandomSource, IsGroup and CanEasilyComputePcgs and IsFinite ],
functionr, grp
 local p IsCollsCollsElms,[IsGroup and CanEasilyComputePcgs IsGroup and

 p :=(H,,)
 if Length( p ) = 0 then
 return One( grp d java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
 else
 return Product( p, x -> x^Random(rs, ,cent # elementary abelian factor, for affine action
 fi;
end );

BindGlobal( "CentralizerSolvableGroup", function(H,U,elm)
local G, home, # the supergroup (of <H> and ), the home pcgs
 Hp, .
 inequal, # G<>H flag
 eas, elementary abelian series in <G> through 
 step, # counter looping over <eas>
L, members of <eas>
 Kp,Lp, # induced and modulo pcgs's
 KcapH,LcapH, # pcgs's of intersections with <H> Hjava.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 15
 N, cent, # elementary abelian factor, for affine action
 cls, # classes in range/source of homomorphism
 opr, # (elm^opr)=cls.representative
 nexpo,indstep,Ldepif not(,NT

 # Treat the case of a trivial group.
 if IsTrivial( U ) then
 return H;
 fi;

 if IsSubgroup( homePcgsElementaryAbelianSeries
 G:=H;
 inequal:=false;
 else
 G:=ClosureGroup( H, U );
 inequal:=true eas:java.lang.StringIndexOutOfBoundsException: Range [14, 13) out of bounds for length 14
 fi;

 home:=HomePcgs(G);
 if not HasIndicesEANormalSteps(home) then
 home:=PcgsElementaryAbelianSeries(G);
 fi;
 # Calculate a (central) elementary abelian series with all pcgs induced
 # w.r.t. <home>.

 if IsPGroup( G ) then
 home:=PcgsCentralSeries(G);
);
java.lang.StringIndexOutOfBoundsException: Range [38, 33) out of bounds for length 40
 I(
 home:=PcgsElementaryAbelianSeries(G#java.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 18
:java.lang.StringIndexOutOfBoundsException: Range [35, 29) out of bounds for length 36
 cent:=PcClassFactorCentralityTest;

 fi; ;
 indstepodjava.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 7

 Hp:=InducedPcgs(home,H);

 # Initialize the algorithm for the trivial group.
 step:=1;
 while IsSubset( eas[ step +
 step:=step + 1;
 od;
 L :=eas[ step ];
 Ldep:=indstep[step];
 Lp:=InducedPcgs(home,L);
 if inequal then
 LcapH:=NormalIntersectionPcgs( home, Hp, Lp );
 =eas[step];

 cls:=[rec( representative:=elm,centralizer:=H,
 centralizerpcgs:=InducedPcgs(home,H) )];
 opr:=One( U );

 # Now go back through the factors by all groups in the elementary abelian
 # series.
 for step in [ step + 1 .. Length( eas ) ] do

 # We apply the homomorphism principle to the homomorphism G/L -> G/K.
 # The actual computations are all done in <G>, factors are
 # represented by modulo pcgs.
 Kp:=Lp;
 L :=eas[ step ];
 Ldep:=indstep[step];
 Lp:=InducedPcgs(home,L );
 N :=Kp mod Lp; # modulo pcgs representing the kernel
 allcent:=cent( 1 .
 if allcent=false then
java.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 28
 fi;

# #T What is this? Obviously it is needed somewhere, but it is
# #T certainly not good programming style. AH
# SetFilterObj( N, IsPcgs );

 if inequal then
 KcapH :=LcapH;
 LcapH :=NormalIntersectionPcgs( home : ( ;
 N!.capH:=KcapH mod LcapH;
 #T See above
# SetFilterObj( N!.capH, IsPcgs );
 else
 Njava.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12
 fi;

 java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 if allcent
 or cent(home, cls[ 1 ].centralizerpcgs, N, Ldep ) then
 cls:=CentralStepClEANS( home,H, U, N, cls[ 1 ], cl := CentralStepClEANS( home,G, H, N, cl,true

 cls:=GeneralStepClEANS( home, ;
 fi;
 opr:=opr * tra := tra=tra*cloperatorjava.lang.StringIndexOutOfBoundsException: Index 33 out of bounds for length 33
 if IsModuloPcgs(cls[1].cengen) then
 cls[1].centralizerpcgs

 cls[1].centralizerpcgs: fijava.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 11
 fi;

 ;

 if not IsBound(cls[1].centralizer) then
 cls[1].cl:=ConjugateSubgroup.entralizer -)java.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 54
 fi;
 cls:= Assert(2,IsSubset)
 return cls return

end );

#############################################################################
##
#M Centralizer( <G>, <g> ) . . . . . . . . . . . . . . using affine methods
##
InstallMethod( CentralizerOp,
 "pcgs i in GeneratorsOfGroup
 IsCollsElms,
 [ od
 G=(,G
 0, # in solvable permutation groups, backtrack seems preferable

function( G, g([java.lang.StringIndexOutOfBoundsException: Range [62, 61) out of bounds for length 72
 java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
end );

InstallMethod(F ElementaryAbelianSeries( <list> )
 "pcgs computable groups",
 IsIdenticalObj,
 [ IsGroup and CanEasilyComputePcgs and IsFinite,
 IsGroup and CanEasilyComputePcgs ,# there is a generic groups function with value 0
 0, # in solvable permutation groups, backtrack seems preferable,i, ,,java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 35

(G )
local h,P;

 P:=Parent 1S(Last()
 S:java.lang.StringIndexOutOfBoundsException: Range [23, 22) out of bounds for length 28
 G := CentralizerSolvableGroup( ;
 od;
 G:=AsSubgroup(P,G);
 Assert(2,ForAll(GeneratorsOfGroup enforce the same parent for 'HomePcgs' purposes.
 j->Comm(iN:[]java.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 18
 return G;
end );

#############################################################################
##
#M RepresentativeAction( <G>, <d>, <e>, OnPoints ) using affine methods
##
InstallOtherMethod( RepresentativeActionOp,
 "element conjugacy in pcgs computable groups", IsCollsElmsElmsX,
 [ IsGroup and InducedPcgs(home
 IsMultiplicativeElementWithInverse,
IsMultiplicativeElementWithInverse
 IsFunction if IsuminNthen
 0,

function( G, d, efi;
 if opr <> OnPoints or not (IsPcGroup(G) or (d ( .java.lang.StringIndexOutOfBoundsException: Range [35, 32) out of bounds for length 35
 not (d in G and e in Gjava.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
 TryNextMethod();
 fi;
 return ClassesSolvableGroup( G, 4,rec(candidates: java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
end );

#############################################################################
##
#M CentralizerModulo(<H>,<N>,<elm>) full preimage of C_(H/N)(elm.N)
##
java.lang.StringIndexOutOfBoundsException: Range [14, 13) out of bounds for length 66
 IsCollsCollsElms,[IsGroup and CanEasilyComputePcgs, IsGroup and
 CanEasilyComputePcgs, Reversed( CanonicalPcgsWrtFamilyPcgs
function(H,NT,elm)
local G, # common parent
 home pInputPcGroup( , <name> ) . . . . . . . . . . . . gap input string
 eas## Return this input as string. The group will be named <name>,the
 ea2, # used for factor series
 L, # members of <eas>
 ,Lp#
 KcapH
 N, cent, # elementary abelian factor, for affine action
 tra, # transversal for candidates
 nexpo,indstep,Ldep,allcent,
 cl, i; # loop variables

 # Treat trivial cases.
 if Index(H,NT)=1 or (HasAbelianFactorGroup(H,NT =java.lang.StringIndexOutOfBoundsException: Range [33, 32) out of bounds for length 36
 or elm in NT then
 return H;
 fi;

 if elm in H then
 G:=H;
 else
 G:=losureGroupH;
 # is the subgroup still normal
 notjava.lang.StringIndexOutOfBoundsException: Range [22, 21) out of bounds for length 32
 Error("subgroupAdd(ines,";=f;\n";
 fi;
 fi;

:HomePcgs)
 if not HasIndicesEANormalSteps(home) then
 home:=PcgsElementaryAbelianSeries(G);
 fi;

 # Calculate a (central) elementary abelian series.

 eas:=fail;
 if IsPGroup( G ) then
 home:=PcgsPCentralSeriesPGroup(G);
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 if NT in eas then
cent ;
 else#
 java.lang.StringIndexOutOfBoundsException: Range [14, 13) out of bounds for length 30
 fi;
 fi;

 k:;
 home:= while k <= Length(list list[]= dok: + 1od;
 eas:=EANormalSeriesByPcgsif>( Ijava.lang.StringIndexOutOfBoundsException: Range [55, 48) out of bounds for length 55
 cent:=PcClassFactorCentralityTest;
 fi;
 indstep:=IndicesEANormalSteps(java.lang.StringIndexOutOfBoundsException: Index 37 out of bounds for length 33

 # series to NT
 ea2:=List(eas,i->str=",);
 eas:= ;
 for for i:java.lang.StringIndexOutOfBoundsException: Range [22, 21) out of bounds for length 32
 if not i in eas then
 Add(eas,i);
 fi;
 od;
 for i in eas do
 if not HasHomePcgs(i) then
 SetHomePcgs(i,ParentPcgs(home list>1 then
 fi;;
 od;

 Hp:=InducedPcgs(home,H);

 # Initialize the algorithm for the trivial group.
 step := 1;
 while IsSubset( eas[ step + 1 ], H ) do
 step := step + 1; :count+Length);
 od;
 L := eas[ step ];
 Lp := InducedPcgs(home, L );
 if not IsIdenticalObj( G, H ) then
gs Hp Lp )java.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for length 56
 fi;

 cl neO()then
 (linesConcatenation",),
 =(,H))java.lang.StringIndexOutOfBoundsException: Index 59 out of bounds for length 59
 tra := One( H l,,"java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 27

# cls := List( candidates, c -> cl );
# tra := List( candidates, c -> One( H ) );
 tra:=One(H);

 # Now go back through the factors by all groups in the elementary abelian
#
 for step in [ step + 1 .. Length( eas ) ] do
 Kp := Lp;
L: [step ;
 Ldep:=indstep[step]; :=ommg[][)java.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 36
 Lp := InducedPcgs(home, L );
 N := Kp mod Lp;
 #SetFilterObj( N, IsPcgs );
 allcent:= (lines,oncatenation""String)""Stringi"",
 if (ne,]")
 nexpo:=LinearActionLayerAddlinesC(""()",i),java.lang.StringIndexOutOfBoundsException: Index 72 out of bounds for length 72
 fi;
 if not IsIdenticalObj( G, H ) then
 KcapH := LcapH;
 LcapH := NormalIntersectionPcgs( home, Hp, Lp );
NcapH : modLcapH;
 else
 N!.capH := N;
 fi;

 cl.candidates := cl.representative;
 if allcent
 or cent(home,cl.centralizerpcgs(")\"java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 23
 cl := CentralStepClEANS( home,G, H lines;
 else
 cl := Add(lines,"Print(
 fi;
 = *
 if IsModuloPcgs(cl.cengen) .
 cl.centralizerpcgs:=cl.cengen;
 else
 cl.centralizerpcgs:=InducedPcgsByPcSequenceNC(home,cl.cengen);
 fi;

 od;

 if not IsBound(cl.centralizer) then
 cl.centralizer:=SubgroupByPcgs(G,cl.centralizerpcgs);
 fi;
 cl:= lines:=newLines
 Assert(2 od
 (2IsSubsetGcl);
 return cl;

end);

InstallMethod(CentralizerModulo,"group centralizer via generators",
 IsFamFamFam,[IsGroup and CanEasilyComputePcgs, IsGroup and
 CanEasilyComputePcgs, IsGroup],0,
function(G,NT,U)
local i,P;
 P:=Parent(G);
 for i in GeneratorsOfGroup(U) do
 G:=CentralizerModulo(G,NT,i);
 od;
 G:=AsSubgroup## otherwise the power presentation.
 return G;
end);

# enforce solvability check.
RedispatchOnCondition(CentralizerModulo,true,[IsGroup,IsGroup,IsObject],
 [IsGroup and InstallGlobalFunction PrintPcPresentation functionGcommBool

#############################################################################
##
#F ElementaryAbelianSeries( <list> )
##
InstallOtherMethod( ElementaryAbelianSeries,"list of pcgs computable groups",
 true,[IsList and IsFinite],
 1, # there is a generic groups function with value 0
function( S )
local home,i, N, O,

( java.lang.StringIndexOutOfBoundsException: Range [46, 44) out of bounds for length 55
 TryNextMethod i+.]
 ;

eck
if<(Last)then
 S := ShallowCopy( S );
 Add( S, TrivialSubgroup(S[1]) java.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 11
 fi;

 # start with the elementary series of the first group of <S>
 L := ElementaryAbelianSeries( S if*] pcgsi *java.lang.StringIndexOutOfBoundsException: Range [51, 49) out of bounds for length 57
 # enforce the same parent for 'HomePcgs' purposes.
 home:=HomePcgs(S[1]);

 N := [ S[ 1 ] ]fi
 for i in [ 2 .. Length( S ) - 1 ] do
 O := L;
 L := [ S[ i ] ];
 for E in O do
 I := IntersectionSumPcgs(home, InducedPcgs(home,E),
 InducedPcgs(home,S[ i ]) );
 I.sum:=SubgroupByPcgs(S[1],I.sum);
 I.
 . Nthen
 Add( N, I.sum );
 fi;
 if not I.intersection in L then
 Add( L, I.############################################################################
 fi;
 od;
 od;
 for E in L do
 if not E in N then
 Add( N, E );
 fi;
 od;
 return N;
end);

#############################################################################
##
#M \<(G,H) . . . . . . . . . . . . . . . . . comparison of pc groups by CGS
##
java.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12
function( G, H if IsAbelian()
 return (G
 < Reversed( java.lang.StringIndexOutOfBoundsException: Index 38 out of bounds for length 36
end);

#############################################################################
##
#F GapInputPcGroup( , <name> ) . . . . . . . . . . . . gap input string
##
## Compute the pc-presentation for a finite polycyclic group as gap input.
## Return this input as string. The group will be named <name>,the
## generators "g".
##
InstallGlobalFunction( GapInputPcGroup, function(U,name)

 local gens,
 wordString,
 newLines,
 lines,
 ne,
 true,

 # <lines> will hold the various lines of the input for gap,they are
 # concatenated later.
 lines:=[];

 # Get the generators for the group .
 :)java.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 36

 # Initialize the group and the generators.
 Add(m
 Add(lines,":=function()\nlocal ");
 for i in [1 .. Length(gens)] do
 Add(lines,"g");
 Add(lines,String(ino# its normalizer
 Add(lines,",");
 od;
 Add(lines,"r,f,g,rws,x;\n");
 Add(lines# p, # orbit pos.
 Add(lines,
 Add(lines,") opcgs,#(

 for i in [1 .. Length(gens)] opfun,# operation function
 Add(lines,java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 :=SubgroupG,(),
Addlinesjava.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length 26
 Add(lines,String(i) ;
 Add(lines,"];\n" );
 od;

l,"=SingleCollector,";
 Add(lines,String(List(gens,i->RelativeOrderOfPcElement(gens,i))));
 Add(,")\n")

 (linesr=n";
 # A function will yield the string for a word.
 wordString:=function(a)
 local k,l,list,str,count;
 list:=ExponentsOfPcElement(gens,a);
 k:=1
 while k <= Length:java.lang.StringIndexOutOfBoundsException: Range [40, 38) out of bounds for length 63
 if k > Length(list) then return List(e-Image)
 if list[k] <> 1 then
 str:=Concatenation("g",String(k),"^if G.java.lang.StringIndexOutOfBoundsException: Range [47, 42) out of bounds for length 47
e:!java.lang.StringIndexOutOfBoundsException: Range [43, 42) out of bounds for length 43
 else
 str:=Concatenation("g",String(k));
 fi;
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 for l in [k + 1 .. Length(list)] do
 if count > 60 then
 str :=Concatenation(# find the largest abelian quotient
 :java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 25
 ;
 count:=count - Length(str);
 if list[l] > 1 then

 String(list[l]));
 elif list[l] = 1 then
 str:=Concatenation(str,"*g",String(l));
 fi;
 count:=count + Length(str);
 od;
 str;
 end

 # Add the power presentation part.
 for in[ .
 ne:=gens[i]^RelativeOrderOfPcElement(java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 if ne<>Oneif then
 Add(lines,Concatenation("[",String(i)#UU:=ShallowCopy(min);
 wordString(java.lang.StringIndexOutOfBoundsException: Range [0, 25) out of bounds for length 16
 if i<Length(gens) then
 # opera
 else
 (mpcgsListu,>^e)
 fi;
 fi;
 od;
 Add(lines,"];\nfor x in r do #if UU<>u then

 Add(lines,"r:=[\n

 # Add the commutator presentation part.
 for i in [1java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8
for[+ .Length(gens)]o
 ne:=Comm(gens[j],gens[i]);
 if ne<>One(U) then
 # this function computes the orbit in a well-defined order that permits
 Add(lines,Concatenation orb:Pcgs_OrbitStabilizer(,,,)
 wordString(ne),"],\n"));
 else
 Add(orb=orb;
 wordString(ne),"]\n"# Error("len!");
 fi;
 fi;
 od;
 od;
in do SetCommutator(([]x2,x[3);n)
 Add(lines,"return GroupByRwsNC(
 (";n)
 Add(lines,name);
 Add(lines,":=");
 Add(lines,name);
 Add(lines,"();\n");
 Add(lines,"Print(\"#I A group of order \",Size(");
 Add(lines,name);
 Add(lines,"),\" has been defined.\\n\");\n");
,Print\It iscalled );
 Add(lines,name);


# nno:=Normalizer(no,fv);
 while Length(lines) > 1 do
 if Length(lines) mod 2 = 1 then
 Add(lines,"");
 fi;
 newLines:=[];
 for i in [1## nocl:=NormalClosure(no,fv);
 newLines[i]:=Concatenation(lines[2*i-1],lines[2*i]);
 od;
 lines:=newLines;
 od;
 IsString(lines[1]);
 return lines[1];

end );

#############################################################################
##
#F PrintPcPresentation( <grp>, <commBool> )
##
## Display the pc relations of a pc group.
## If <commBool> is true, then the commutator presentation is printed,
## otherwise the power presentation.
## Trivial commutators / powers are not printed.
## The generators are named "g".
## The returned boolean indicates if there are commuting generators.
##
InstallGlobalFunction( PrintPcPresentation, function(G, commBool)
 local pcgs, n, F, gens, i, pis, exp, t, h, commPower# orb:=Product([1..Length(orb)],i->lop[i]^orb[i]);

 pcgs:=Pcgs(G);
 n:=Length(pcgs);
 F := FreeGroup( n, "g" );
 gens := GeneratorsOfGroup( F );
 pis := RelativeOrders# fi;

 # compute the orders of the pc-generators
 for i in [1..n] do
 exp := ExponentsOfRelativePower# NORMALIZE_IGS(mpcgs,min);
 # minrep:=one;
 for h in [i+1..n] do
 t := t * gens[h]^exp[h-i];
 od;
 if IsOne( t ) then
 t := "id";
 fi;
 Print(gens[i], "^", pis[i], " = ", t, "\n");
 od;

 # compute the commutators / conjugation
 # of all pairs of pc-generators
 trivialCommutators := false;
 for i in [1..n] do
 for j in [i+1..n] do
 if pcgs[j] * pcgs[i] = pcgs[i] * pcgs[j] then
 trivialCommutators := true;
 continue;
 fi;
 if commBool then
 commPower := Comm( pcgs[j# minrep:=o;
 else
 commPower := pcgs[j]^pcgs[i]# fi;
 fi;
 exp := ExponentsOfPcElement( pcgs, commPower ){[i+1..n]};
 t := One( F );
 for h in [i+1..n] do
 t := t * gens[h]^exp[h-i :=java.lang.StringIndexOutOfBoundsException: Range [21, 20) out of bounds for length 46
 od;
 if commBool then
 Print("[", gens V:=PreImage(iso,V);
 else
 Print(gens[j], "^", gens[i]);
 fi;
 Print(" = ", t, "\n");
 od;
 od;

 java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 6
end );

#############################################################################
##
#M Display( <grp> )
##
InstallMethod( Display,
 "for a pc group",
 [ IsPcGroup ],
 function( G )
 local n, function(,U)
 if IsTrivial(G) then
 Print("trivial pc-group\n");
 return;
 fi;
 n := Size(Pcgs(G));
 if IsOne(n) then
 Print("cyclic pc-group with 1 pc-generator and the relation:
 (cl,G;
 SetRepresentativecl,)
 fi;
java.lang.StringIndexOutOfBoundsException: Range [30, 26) out of bounds for length 62
 java.lang.StringIndexOutOfBoundsException: Range [11, 10) out of bounds for length 14
 Print("java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 then
 (java.lang.StringIndexOutOfBoundsException: Range [27, 26) out of bounds for length 59
 fi;
 endOnPoints IsSubsetGU)andIsSubset(,) then

#############################################################################
##
#M Enumerator( <G> ) . . . . . . . . . . . . . . . . . . enumerator by pcgs
##
llMethod( Enumerator,"finite pc computable groups",true,
 [ IsGroup and CanEasilyComputePcgs and IsFinite ], 0,
 G -> EnumeratorByPcgs( Pcgs( G ) ) );

#############################################################################
##
#M KnowsHowToDecompose( <G>, <gens> )
##
InstallMethodc1[]c2[]
 "pc group and generators: always true",
 #############################################################################
 [ IsPcGroup, IsList ], 0,
 ##

#############################################################################
##
#F CanonicalSubgroupRepresentativePcGroup( <G>, )
##
InstallGlobalFunction( CanonicalSubgroupRepresentativePcGroup,
 function(G,U)
local e, # EAS
 pcgs, # himself
 iso, # isomorphism to EAS group
 start, # index of largest abelian quotient
 i, # loop
 m, # e[i+1]
 pcgsm, # pcgs(m)
 mpcgs, # pcgs mod pcgsm
 if Sizeser[i])<izen) then
 fv, # <V,m>
 fvgens, # gens(fv)
 no, # its normalizer
 orb, # orbit
 ,
 nno, # growing normalizer
 min,
 minrep, # minimum indicator
 p, # orbit pos.
 one, # 1
 abc, # abelian case indicator
 nopcgs, #pcgs(no)
 te, # transversal exponents
 opfun, # operation function
 ce; # conj. elm

 if not IsSubgroup(G,U) then
 Error("#W CSR Closure\n");
 :Subgroup(Parent(G),Concatenation(GeneratorsOfGroup(G),
 GeneratorsOfGroup(U)));
 fi;

 # compute a pcgs fitting the EAS
 pcgs:=PcgsChiefSeries(G);
 e:=ChiefNormalSeriesByPcgs(pcgs);

 if not IsBound(G!.java.lang.StringIndexOutOfBoundsException: Range [58, 49) out of bounds for length 58
 # test whether pcgs is family induced
 m:=List(pcgs,i->ExponentsOfPcElement(FamilyPcgs(java.lang.StringIndexOutOfBoundsException: Index 53 out of bounds for length 10
 G!.chiefSeriesPcgsIsFamilyInduced:=
 ForAll(m,i->Number(i,j->j<>0)=1) and ForAll(m,java.lang.StringIndexOutOfBoundsException: Index 53 out of bounds for length 9
 and m=Reversed(Set(m));
 not . then
 # compute isom. &c.
 V:=PcGroupWithPcgs(pcgs);
roupHomomorphismByImagesNC(G,V,pcgs,FamilyPcgs(V));
 G!.isomorphismChiefSeries:=iso;
 G!.isomorphismChiefSeriesPcgs:=FamilyPcgs(Image(iso));
 G!.isomorphismChiefSeriesPcgsSeries:=List(e,i-Image(iso,i));
 fi;
 fi;

 if not G!.chiefSeriesPcgsIsFamilyInduced then
 iso:=G!.isomorphismChiefSeries;
 pcgs:=G!.isomorphismChiefSeriesPcgs;
 e:=G!.isomorphismChiefSeriesPcgsSeries;
 U:=Image(iso,U);
 G:=Image(iso);
 else
 iso:=false;
 fi;

 #pcgs:=Concatenation(List([1..Length(e)-1],i->
 # InducedPcgs(home,e[i]) mod InducedPcgs(home,e[i+1])));
 #pcgs:=PcgsByPcSequence(ElementsFamily(FamilyObj(G)),pcgs);
 ##AH evtl. noch neue Gruppe

 # find the largest abelian quotient
 start:=2;
 while start<Length(e) and HasAbelianFactorGroup
 start:=start+1;
 od;

 #initialize
 V:=U;
 one:=One(G);
 ce:=One(G);
 no:=G;

 for i in [start..Length(e)-1] do
 # lift from G/e[i] to G/e[i+1]
 m:=e[i+1];
 pcgsm
 mpcgs:=pcgs mod pcgsm;

 # map v,no
 #fv:=ClosureGroup(m,V);
 #img:=CanonicalPcgs(InducedPcgsByGenerators(pcgs,GeneratorsOfGroup(fv)));

# if true then

 nopcgs:= / GAPInfo. > 50

 fvgens:=GeneratorsOfGroup(V);
 if true then
 (java.lang.StringIndexOutOfBoundsException: Range [20, 16) out of bounds for length 57
#UU:=ShallowCopy(min);
# NORMALIZE_IGS(mpcgs,min);
#if UU<>min then
# Error("hier1");
#fi;
 # trim m-part
)

 # operation function: operate on the cgs modulo m
 opfun:=function(u,e)
 u:=CorrespondingGeneratorsByModuloPcgs(mpcgs,#M CanEasilyComputePcgs( <pcgrp> ) . . . . . . . . . . . . . . . . pc group
#UU:=ShallowCopy(u);
# NORMALIZE_IGS(mpcgs,u);
#if UU<>u then
# Error("hier2");
#fi;

 # trim m-part
 u:=List(u,i->CanonicalPcElement(pcgsm(CanEasilyComputePcgsIsGroup java.lang.StringIndexOutOfBoundsException: Range [67, 66) out of bounds for length 69
 return u;
 end;
 else
 min#M CanEasilyTestMembership
 opfun:=OnPoints;
 fi;

 # this function computes the orbit in a well-defined order that permits
 # to find a transversal cheaply
 orb:=Pcgs_OrbitStabilizer(nopcgs,false,min,nopcgs,opfun);

 nno:=orb.stabpcgs;
 abc:=orb.lengths;
 orb:=orb.orbit;
#if Length(orb)<>Index(no,Normalizer(no,fv)) then
# Error("len!");
#fi;

 # determine minimal conjugate
 minrep:=one;
 for o in [2..Length(orb)] do
 if orb[o]<min then
 min:=orb[o];
 minrep:=o;
 fi;
 od;

 # compute representative
 if IsInt(minrep) then
 te:=ListWithIdenticalEntries(Length(nopcgs),0);
 o:=2;
 while minrep<>1 do
 while abc[o]## they should *not* inherit `CanEasilyComputePcgs' automatically.
 o:=o+1;
 od;
 te[o-1]:=-QuoInt(minrep-1,abc[o]);
 minrep:=(minrep-1) mod abc[o]+1;
 od;
 te:=LinearCombinationPcgs(nopcgs,te)^-1;
 if opfun(orb[1],te)<>min then
 Error("wrong repres!");
 fi;
 minrep:=te;
 fi;

#
#
# nno:=Normalizer(no,fv);
#
# rep:=RightTransversal(no,nno);
# #orb:=List(rep,i->CanonicalPcgs(InducedPcgs(pcgs,fv^i)));
#
# # try to cope with action on vector space (long orbit)
## abc:=false;
## if Index(fv,m)>1 and HasElementaryAbelianFactorGroup(fv,m) then
## nocl:=NormalClosure(no,fv);
## if HasElementaryAbelianFactorGroup(nocl,m) then
### abc:=true; # try el. ab. case
## fi;;
## fi;
#
# if abc then
# nocl:=InducedPcgs(pcgs,nocl) mod pcgsm;
# nopcgs:=InducedPcgs(pcgs,no) mod pcgsm;
# lop:=LinearActionLayer(Group(nopcgs),nocl); #matrices for action
# fvgens:=List(fvgens,i->ShallowCopy(
# ExponentsOfPcElement(nocl,i)*Z(RelativeOrders(nocl)[1])^0));
# TriangulizeMat(fvgens); # canonize
# min:=fvgens;
# minrep:=one;
# for o in rep do
# if o<>one then
# # matrix image of rep
# orb:=ExponentsOfPcElement(nopcgs,o);
# orb:=Product([1..Length(orb)],i->lop[i]^orb[i]);
# orb:=List(fvgens*orb,ShallowCopy);
# TriangulizeMat(orb);
# if orb<min then
# min:=orb;
# minrep:=o;
# fi;
# fi;
# od;
#
# else
# min:=CorrespondingGeneratorsByModuloPcgs(mpcgs,fvgens);
# NORMALIZE_IGS(mpcgs,min);
# minrep:=one;
# for o in rep do
# if o<>one then
# if Length(fvgens)=1 then
# orb:=fvgens[1]^o;
# orb:=orb^(1/LeadingExponentOfPcElement(mpcgs,orb)
# mod RelativeOrderOfPcElement(mpcgs,orb));
# orb:=[orb];
# else
# orb:=CorrespondingGeneratorsByModuloPcgs(mpcgs,List(fvgens,j->j^o));
# NORMALIZE_IGS(mpcgs,orb);
# fi;
# if orb<min then
# min:=orb;
# minrep:=o;
# fi;
# fi;
# od;
# fi;

 tonew minimal one
 no:=ClosureGroup(m,List(nno,i->i^minrep));
 ce:=ce*minrep;
 matrix:=List([1.((G),g-ExponentsOfRelativePower(PcgsG,g);
 od;

 if iso<>false then
 V:=PreImage(iso,V);
 no:=PreImage(iso,no);
 ce:=PreImagesRepresentative(iso ;
 fi;
 return [V,no,ce];
endord:[

#############################################################################
##
#M ConjugacyClassSubgroups(<G>,<g>) . . . . . . . constructor for pc groups
## This method installs 'CanonicalSubgroupRepresentativePcGroup' as
## CanonicalRepresentativeDeterminator
##
InstallMethod(java.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 7
function(G,U)
local cl;

 cl:=Objectify(NewType##
 IsConjugacyClassSubgroupsByStabilizerRep),rec());
 SetActingDomain(cl,G);
 SetRepresentative(InstallMethod(MinimalGeneratingSet,
 SetFunctionAction(cl,OnPoints);
 SetCanonicalRepresentativeDeterminatorOfExternalSet(cl,
 CanonicalSubgroupRepresentativePcGroup);
 return cl;
end

InstallOtherMethod(RepresentativeActionOp local pcgs matrix,snfgens cti, ,ijava.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 54
 [IsPcGroup,IsPcGroup,IsPcGroup,java.lang.StringIndexOutOfBoundsException: Index 39 out of bounds for length 22
function(G,U,V,java.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 0
local c1,c2;
 if f<>OnPoints or not (IsSubset(G,U) and IsSubsetmatrixii=java.lang.StringIndexOutOfBoundsException: Range [42, 41) out of bounds for length 51
 TryNextMethod();
 fi;
 if Size(U)<>Size(V) then
 return fail;
 fi;
 c1:=CanonicalSubgroupRepresentativePcGroup
 c2:=CanonicalSubgroupRepresentativePcGroup(G,V);
 if c1[1]<>c2[1] then
 return fail;
 fi;
 return c1[3]/c2[3];
end);

#############################################################################
##
#F ChiefSeriesUnderAction( , <G> )
##
InstallMethod#############################################################################
 "method for a pcgs computable group",
 IsIdenticalObj,

function( U, G # Return exponent and probably also an element of high order. If exponent is
local home,e,ser,i,j,k,pcgs,mpcgs,op,m,cs,n;
 home:=HomePcgs(G);
 e:=# JS: A result of Higman detailed on p564 of C. Sims Computation with

 # make the series U-invariant
 ser:=ShallowCopy(e);
 e:=[G];
 n:=G;
 for # generator with a normed row vector for exponents.
 # check whether we actually stepped down (or did the intersection
 # already do it?
 if Size(ser[i])<Size(n) then
 if not IsNormal(U,ser[i]) then
 # assuming the last was normal we intersect the conjugates and get a
 # new normal with still ea. factor
 [i]=(,ser[)
 # intersect the rest of the series.
 for j in [i+1..Length(ser)-1] do
 ser[j]:=Intersection(ser[i],ser[j]);
 od;
fi
 Addc=java.lang.StringIndexOutOfBoundsException: Range [29, 28) out of bounds for length 32
 n:=ser[i];
 fi;
 java.lang.StringIndexOutOfBoundsException: Range [24, 1) out of bounds for length 37

 :G
 for i in [2..odjava.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19
 Info(InfoPcGroup,1,"Step ",java.lang.StringIndexOutOfBoundsException: Range [0, 32) out of bounds for length 12
 if IsPrimeInt(Indexei1,e[i])then
 Add(ser,e[i]);
 else
 pcgs:=InducedPcgs(home,e[i-1]);
cgshomeei];
 op:=LinearActionLayer(U,GeneratorsOfGroup(U),mpcgs);
 if ForAll(op,IsOne) then
 m:=op[1]; # identity
 cs:=List([0..Length(m) ldim]=Minimum -,(w+1)
 else
 m:=GModuleByMats(op,GF(RelativeOrderOfPcElement(mpcgs,mpcgs[1])));
 cs:=MTX.BasesCompositionSeries(m);
 fi;
 Sort(cs,function(a,b) return Length(a)>Length(b);end);
 cs: java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 25
 Info(InfoPcGroup,2,Length( thenreturn [,()]; ;
 for j in cs do
 =java.lang.StringIndexOutOfBoundsException: Range [26, 25) out of bounds for length 35
 for k in j do
 [class,First(pcgs,g->Order(g)=pclass)]java.lang.StringIndexOutOfBoundsException: Index 63 out of bounds for length 63
 od;
 Add(ser,n);
 java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
 fi;
java.lang.StringIndexOutOfBoundsException: Range [11, 10) out of bounds for length 48
 return ser;
end);

InstallMethod(#############################################################################
 [IsSolvableGroup],
 # this is also better for permutation groups, so we increase the value to t,java.lang.StringIndexOutOfBoundsException: Range [50, 49) out of bounds for length 74
 # be above the value for `IsPermGroup'.
 {} -> Maximum(RankFilter(IsSolvableGroup),
 RankFilter(IsPermGroup
IsSolvableGroup
()
 return IsInt(Size(G)) and IsPrimeInt(Size(G)java.lang.StringIndexOutOfBoundsException: Index 46 out of bounds for length 31
end);

#############################################################################
##
#M ViewObj(<G>)
##
InstallMethod(ViewObj:java.lang.StringIndexOutOfBoundsException: Range [15, 14) out of bounds for length 16
function(G)
local nrgens;
 nrgens := Length(GeneratorsOfGroup(G));
 if (not HasParent(G)) or
 nrgens*Length(GeneratorsOfGroup(Parent(G)))
 / GAPInfo.ViewLengthf;
 Print("<pc group");
 if HasSize(G) then
 Print(" of size ",Size(G));
 fi;
 Print(" with ", Pluralize(nrgens, "generator"), ">");
 else
 Print("Group(");
 ViewObj(GeneratorsOfGroup(G));
 Print(")");
 fi;
end);

#############################################################################
##
#M CanEasilyComputePcgs( <pcgrp> ) . . . . . . . . . . . . . . . . pc group
##

InstallTrueMethod # The following method is due to Jack Schmidt

# InstallTrueMethod( CanEasilyComputePcgs, HasPcgs );
# we cannot guarantee that computations with any pcgs is efficient

java.lang.StringIndexOutOfBoundsException: Range [39, 17) out of bounds for length 69

#############################################################################
##
#M CanEasilyTestMembership
##

# InstallTrueMethod(CanEasilyTestMembership,CanEasilyComputePcgs);
# we cannot test membership using a pcgs

# InstallTrueMethod(CanComputeSize, CanEasilyComputePcgs); #unnecessary

#############################################################################
##
#M IsSolvableGroup
##
InstallTrueMethod gwhile gp^)) =^;; java.lang.StringIndexOutOfBoundsException: Range [72, 71) out of bounds for length 79

#############################################################################
##
#M CanComputeSizeAnySubgroup
##
InstallTrueMethod( CanComputeSizeAnySubgroup, CanEasilyComputePcgs:java.lang.StringIndexOutOfBoundsException: Range [23, 22) out of bounds for length 28

#############################################################################
##
#M CanEasilyComputePcgs( <grp> ) . . . . . . . . . subset or factor relation
##
## Since factor groups might be in a different representation,
## they should *not* inherit `CanEasilyComputePcgs' automatically.
##
#InstallSubsetMaintenance( CanEasilyComputePcgs,
# IsGroup and CanEasilyComputePcgs, IsGroup );

#############################################################################
##
#M IsConjugatorIsomorphism( <hom> )
##
InstallMethod( IsConjugatorIsomorphism,
 "for a pc group general mapping",
 true,
 [ IsGroupGeneralMapping ], 1,
 # There is no filter to test whether source and range of a homomorphism
 # are pc groups.
this method
 # higher ranking than the default one in `ghom.gi'.
 function( hom )

 local s, r# Efficiency notes:

 s:= Source( hom );
 if not IsPcGroup( s ) then
 TryNextMethod();
# (2) "SubgroupByPcgs(G,Pcgs(...))" is used to give the returned subgroup
 return false;
 elif IsEndoGeneralMapping( java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 return true;
 fi;
 r:= Range( hom );

 #
 if FamilyObj( s ) <> FamilyObj( r ) then
 return false;
 fi;

 # Compute a conjugator in the full pc group.
 G:= GroupOfPcgs( FamilyPcgsjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 genss:= GeneratorsOfGroup( s );
 rep:= RepresentativeAction( G, genss, List( genss,
 i -> ImagesRepresentative( hom, i ) ), OnTuples );

 # Return the result.
 if rep <> fail then
 Assert( 1, ForAll( genss, i -> Image( hom, i ) = i^rep ) );
 SetConjugatorOfConjugatorIsomorphism( hom, rep );
 return true;
 else
 return false;
 fi;
 end );

#############################################################################
##
#M CanEasilyComputeWithIndependentGensAbelianGroup( <pcgrp> )
##
InstallTrueMethod(CanEasilyComputeWithIndependentGensAbelianGroup,


#############################################################################
##
#M IndependentGeneratorsOfAbelianGroup( <A> )
##
InstallMethod(IndependentGeneratorsOfAbelianGroup#
 "# Assumed: G is a p-group, e is a positive integer
 [IsGroup and CanEasilyComputePcgs and IsAbelian],0,
function(G)
local matrix, snf, base, ord, cti, row, g, o, cf#Choose a central element z of order p. Suppose that by induction

 if IsTrivial(G) then return []; fi;

 matrix:=List([1..Size(Pcgs(G))],g->List(ExponentsOfRelativePower(Pcgs(G),g)));
 for#that random methods combined with deterministic computations would
 matrix[i][i]:=-RelativeOrders(Pcgs(G))[i];
 od;
malFormIntMatm18)

 base:=[];
 ord:=[];
 cti:= timerFun :
 for i in [1(G) returnG;fi
 row:=cti[i];
 g:=LinearCombinationPcgs(Pcgs,e;
 if not IsOne(g) then
 # get the involved prime factors
 o:=snf.java.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 0
 cf:=Collected(Factors(o));
if(cf>1 java.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length 26
 for j in cf do
 j:=j[1]^j[2];
 Add(ord,j);
 Add(base,g^(o/j));
 od;
 else
 Add(base,g);
Add(rd,;
 fi;
 fi;
 od;
 SortParallel# or waste a lot of time.
 return r=imerFunc(;
end);

#############################################################################
##
#M MinimalGeneratingSet( <A> )
##
InstallMethod(MinimalGeneratingSet,
 "ompute via ",
 [IsGroup and CanEasilyComputePcgs and IsAbelian], {} -> RankFilter(IsPcGroup),
 function(G)

 local pcgs, matrix, snf, gens, cti, row, g, i;

 if IsTrivial (G) then
 return [];
 fi;

 pcgs := Pcgs#java.lang.StringIndexOutOfBoundsException: Index 92 out of bounds for length 92
 matrix:=List([1..Length
 for i in [1..Length(pcgs)] do
 matrix[]i=RelativeOrders)i];
 od;
 snf:=NormalFormIntMat(matrix,1+8+16);

 gens:=[];
 cti:=snf.coltrans^-1;
 for i in [1..Length(cti)] do
 row:=cti[i];
 g:=Product( List([1..Length(row)],j->pcgs[j]^row[j]));
 if not IsOne(g) then
 Add(gens,g);
 fi;
 od;

 return gens;
 end);

#############################################################################
##
#M ExponentOfPGroupAndElm( <G>, <bound> )
##

# Return exponent and probably also an element of high order. If exponent is
# found to be larger than bound, just return the result found so far.
#
# JS: A result of Higman detailed on p564 of C. Sims Computation with
# F. P. Groups shows that an element of maximal order in a p-group
# exists where its weight with respect to a special pcgs is at most
# the p-class of the group. Furthermore we need only check normed
# row vectors as exponent vectors since every cyclic subgroup has a
# generator with a normed row vector for exponents.
#
# This function just checks all such vectors using a simple backtrack
# method. It handles the case of the trivial group and a regular
# p-group specially.
#
# Assumed: G is a p-group, of max size p^30 or so.
BindGlobal("ExponentOfPGroupAndElm",
function(G,bound)
 local all,pcgs,monic,weights,pclass,p;
 monic := function(w,p,f)
 : ()java.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 28
 M := [0,0];
 c := Maximum(w);
w)
 a := ListWithIdenticalEntries(Size(w),0);
 a[ldim] := 1;
 M1 := all(ldim,a,w return ( , )java.lang.StringIndexOutOfBoundsException: Index 33 out of bounds for length 33
 if M1[1] > M if PrimePGroup()=
 od;
 return M;
 end;
all: (,,wp,,java.lang.StringIndexOutOfBoundsException: Index 39 out of bounds for length 39
 local M,M1;
 if ldim = Size(a) then return [f(a),PcElementByExponents(pcgs,a)]; fi;
 M := [0,0];

java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 while a[ldim+1] >= 0 do
##
 if M1[1] > M[1] then M:=M1; if M[1] IsGroupand IsFinite ,java.lang.StringIndexOutOfBoundsException: Index 58 out of bounds for length 58
 a[ldim+1] := a[ldim+1]-1;
 od;
 return M;
 end;
 p := PrimePGroup(G);
 if p = fail then return [1,One(G)]; fi; # handle trivial p-group of size 1
 pcgs := SpecialPcgs(G);
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 pclass := Maximum(weights);
 if pclass ##
 [IsGroup and IsSol java.lang.StringIndexOutOfBoundsException: Range [57, 55) out of bounds for length 60
 return [pclass,First(pcgs, IsomorphismPcGroup)
 fi;
 bound := Minimum(p^(pclass-1),bound);
 return monic(LGLayers(pcgs),PrimePGroup############################################################################
end);

InstallMethod( Exponent,"finite solvable group",
 true,[IsGroup and IsSolvableGroup and IsFinite],0,
function(G)
 if IsPGroup(G) then
 return ExponentOfPGroupAndElm(G,Size(G))[1];
 fi;
 TryNextMethod();
end);

#############################################################################
##
#M AgemoOp( <G> )
##
( ,""true, , ,,
function( G, p, n )
localjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

 q := p ^ n;
 # if <G> is abelian, raise the generators to the q.th power##
 if IsAbelian(G) then
 return SubgroupNC( G,Filtered( List( GeneratorsOfGroup( G ), x ->
 x^q ),i->not IsOne(i)) );
 fi;

 # based on Code by Jack Schmidt
 PcgsGjava.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 16
 ex:=One(G);
alClosure,ubgroupNCGFilteredList(,->i^),><ex))
 hom:= SizeG)=100 Size()64 then
 f:=Range(hom);
 ex:=ExponentOfPGroupAndElm(f,q);
 while ex[1]>q do
 # take the element of highest order in f and take power of its preimage
 ex:=PreImagesRepresentative(hom,ex[2]^q);
 sub:=NormalClosure(G,ClosureSubgroupNC(sub,ex));
 =(Gsub;
 f:=Range(hom);
 ex:=ExponentOfPGroupAndElm(f,q);
 od;
 return subjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

 # otherwise compute the conjugacy classes of elements
 C := Set( ConjugacyClasses(G), x -> Representative(x)^q );
 return NormalClosure( G, SubgroupNC( G, C ) );
end );

(,for -,,IsPGroup]0,
function(G)
 if IsTrivial(G) then return G; fi;
 return Omega(Center(G),PrimePGroup(G),1);
end);

#############################################################################
##
#M OmegaOp( <G>, , <n> ) . . . . . . . . . . . . for p-groups
##
## The following method is due to Jack Schmidt
## Omega(G,p,e) is defined to be <g in G: g^(p^e)=1>

# Omega_LowerBound returns a subgroup of Omega(G,p,e)
# Assumed: G is a p-group, e is a positive integer
BindGlobal("Omega_LowerBound_RANDOM",100); # number of random elements to test
BindGlobal("Omega_LowerBound",
d:[d1[1](d2-Size((x,]1])1]
local InfoPcGroup,1Subdirect "List(,Size()(x)))
:=unctiong notIsOne^(^) do:=gp od; g;end
 H:=Subgroup d=List(,x>(Imagex));
 H:=ClosureGroup(H,List( :List(1,]x-ListGeneratorsOfGroupG,
 -ImagesRepresentative[](isox]y)))
end);

# Omega_Search is a brute force search for Omega.
# One can search by coset if Omega(G) = { g in G : g^(p^e) = 1 }
# This is the case in regular p groups.
# Assumed: G is a p-group, e is a positive integer
(Omega_Search
function(G,p,e)
local g,H,fix_order,T;
 H:=Omega_LowerBound(G,p,e);
 fix_order:=function(g) while not IsOne(g^(p^e Assert1,sBijective);
 if NilpotencyClassOfGroup(G) Product-y1^[)
 if(g in H) then continue; fi;
 H:=ClosureSubgroup(H,g);
 if(H=G) then returnInfo,,(,>1)
 od;
 return H;
end);

# Omega_UpperBoundAbelianQuotient(G,p,e) returns a subgroup K<=G
# such that Omega(G,p,e) <= K. Then Omega(K,p,e)=Omega(G,p,e)
# allowing other methods to work on a smaller group.
#
# It is not guaranteed that K is a proper subgroup of G.
#
# In detail: Omega(G/[G,G],p,e) = K/[G,G] and K is returned.
#
# Assumed: G is a p-group, e is a positive integer

BindGlobal("Omega_UpperBoundAbelianQuotient",
function(G,p,e)
local f;
 f:=MaximalAbelianQuotient(G);
 IsAbelian(Image(f));
 return SubgroupByPcgsod;
end);

# Efficiency notes:
#
# (1) "PreImagesSet" is used to find the preimage of Omega in G/[G,G].
# there may very well be faster ways of doing this.
#
# (2) "SubgroupByPcgs(G,Pcgs(...))" is used to give the returned subgroup
# with natural standard generators. There may be better ways of doing this,
# and this may not be needed at all.

# Omega_UpperBoundCentralQuotient(G,p,e) returns
# a subgroup K with Omega(G,p,e) <= K <= G. The
# algorithm is (moderately) randomized.
#
# The algorithm is NOT fast.
#
# In detail a random central element, z, of order p is
# selected and K is returned where K/<z> = Omega(G/<z>,p,e).
#
# Assumed: G is a p-group, e is a positive integer

BindGlobal("Omega_UpperBoundCentralQuotient",
function(G,p,e)
local z,f;

 z:=One(G); while(IsOne(z)) do z:=Random(Socle(G)); od;

:NaturalHomomorphismByNormalSubgroup,(,z]);
 IsAbelian(Image(f)); # Probably is not, but quick to check
 return SubgroupByPcgs(G,Pcgs(PreImagesSet(f,Omega(Image(f),p,e))));
end);

# Efficiency Points:
#
# (1) "Omega" is used to compute Omega(G/<z>,p,e). |G/<z>| = |G|/p.
# This is a very tiny reduction AND it is very possible for
# Omega(G/<z>)=G/<z> for every nontrivial element z of the socle without
# Omega(G)=G. Hence the calculation of Omega(G/<z>) may take a very
# long time AND may prove worthless.
#
# (2) "PreImagesSet" is used to calculate the preimage of Omega(G/<z>)
# there may be more efficient methods to do this. I have noticed a very
# wide spread of times for the various PreImage functions.

# Omega(G,p,e) is a normal, characteristic, fully invariant subgroup that
# behaves nicely under group homomorphisms. In particular
# if Omega(G/N)=K/N then Omega(G) <= K. If Omega(G) <= K,
# then Omega(G)=Omega(K).
#
# Hence the general strategy is to find good upper bounds K for
# Omega(G), and then compute Omega(K) instead. It is difficult
# to tell when one's upper bound is actually equal to Omega(G),
# so we attempt to terminate early by finding good lower bounds
# H as well.
#
# Assumed: G is a p-group, e is a positive integer
BindGlobal("Omega_Sims_CENTRAL",100);
BindGlobal("Omega_Sims_RUNTIME",5000);

#Choose a central element z of order p. Suppose that by induction
#we know H = Omega(G/<z>). Then Omega(G) is contained in the inverse
#image K of H in G. Compute K/K'. If that quotient has elements of
#order p^2, then we can cut K down a bit. Thus we may assume that we
#know a normal subgroup K of G that contains Omega(G), K maps into
#H, and K/K' has exponent p. One would hope that K is small enough
#that random methods combined with deterministic computations would
#make it possible to compute Omega(K) = Omega(G).
#-Charles Sims
BindGlobal("Omega_Sims",
function(G,p,e)
local H,K,Knew,fails,r, timerFunc;

 timerFunc := GET_TIMER_FROM_ReproducibleBehaviour();

 if(IsTrivial(G)) then return G; fi;

 K:=G;
 H:=Omega_LowerBound(K,p,e);
 if(H=K) then return K; fi;

 # Step 1, reduce until K/K' = Omega(K/K') then Omega(G)=Omega(K)
 while (true) do # there is a `break' below
 Knew:=Omega_UpperBoundAbelianQuotient(K,p,e);
 if(Knew=K) then break; fi;
 K:=Knew;
 od;

 if (H=K) then
 return K;
 fi;

 # Step 2, reduce until we have fail lots of times in a row
 # or waste a lot of time.
 r:=timerFunc();
 fails:=0;
 while(fails<Omega_Sims_CENTRAL and timerFunc()-r<Omega_Sims_RUNTIME) do
 Knew:=Omega_UpperBoundCentralQuotient(K,p,e);
 if(K=Knew) then fails:=fails+1; continue; fi;
 fails#### This file is part of GAP, a system for computational discrete algebra.
 K:=Knew;
ifH=K) H;;
 od;

 # Step 3: Repeat step 1
 java.lang.StringIndexOutOfBoundsException: Range [8, 7) out of bounds for length 16
java.lang.StringIndexOutOfBoundsException: Range [14, 13) out of bounds for length 62
) break ;
 =;
 (,,
 if(H=return;

#
> returnp) java.lang.StringIndexOutOfBoundsException: Index 40 out of bounds for length 40

 # Otherwise we try to search.
 (G)<24then returnOmega_SearchG,);fi


 # to continue we can try and return a lower bound, but this is too small,1;
 while i < Length(arg) and join <> fail do
method.You return;'ifwish to \"
java.lang.StringIndexOutOfBoundsException: Index 59 out of bounds for length 59
 return Hjava.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
end);

(OmegaOp,java.lang.StringIndexOutOfBoundsException: Index 45 out of bounds for length 45
[ 0,
function G,n )
local gens, q, , ord;

 # trivial cases
 n0java.lang.StringIndexOutOfBoundsException: Range [21, 20) out of bounds for length 43

 if IsAbelian( G ) then

 gens := ,";
 for java.lang.StringIndexOutOfBoundsException: Range [0, 11) out of bounds for length 5
 ( )
 o := GcdInt( [IsPartialPerm, IsPosInt and ],
 o < 1
 Add 1java.lang.StringIndexOutOfBoundsException: Range [45, 44) out of bounds for length 48
 fie)
 od;
returnG,)java.lang.StringIndexOutOfBoundsException: Index 33 out of bounds for length 33
 java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5

 if java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 0
 TryNextMethod();
 ;

ifPcgsG,-((^))then
 returnjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 ()215)then

 else
return Omega_Sims(pn;
 fi;i =new;
end);

############################################################################
##
#M HallSubgroupOp (<grp>, <pi>)
##
InstallMethodInstallMethod(PartialPermOpNC " object, list, function",
[IsGroup andIsSolvableGroup and IsFinite, IsList], 0,
 function (grp, pi)
 localiso;
 iso : IsomorphismPcGroup (rp;
returnjava.lang.StringIndexOutOfBoundsException: Range [28, 27) out of bounds for length 73
)

############################################################################
##
#M HallSubgroupOp (<grp>, <pi>)
##
HallSubgroupOp[]java.lang.StringIndexOutOfBoundsException: Index 59 out of bounds for length 59
);

############################################################################
##
#M SylowComplementOp (<grp>, )
##
InstallMethod (SylowComplementOp:arg;
 [IsGroup and IsSolvableGroup =Maximumjava.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 29
 function;
 local iso;
 iso := : (;
 returnPreImagesSet (iso, SylowComplement (ImagesSource (iso), p));
 end returnDensePartialPermNC(ut;

############################################################################
##
#M SylowComplementOp (<grp>, )
##
RedispatchOnCondition(SylowComplementOp,true,[IsGroup,IsPosInt],
and IsFinite,
 IsPosInt ],1 ( )java.lang.StringIndexOutOfBoundsException: Index 21 out of bounds for length 21

(FittingFreeLiftSetup " , IsPcGroup0
java.lang.StringIndexOutOfBoundsException: Index 2 out of bounds for length 0
local java.lang.StringIndexOutOfBoundsException: Range [11, 10) out of bounds for length 38

 pcgs:=java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 0
 return (pcgs:=cgs
 depths:=IndicesEANormalSteps(pcgs),
 radical:=G,
 :G,
 factorhom:= "integers andzero must ",

end)

#############################################################################
##
#M IsomorphismPermGroup( <G> ) . . . . . . . . . for solvable group
##
InstallMethod( return STRINGIFY("PartialPerm(f,""
 "solvableInstallMethod(, "fora partial ",
[ IsGroupand and and CanEasilyComputePcgs ],

local
IsAbelianG
 # force redispatch on abelian group
 java.lang.StringIndexOutOfBoundsException: Range [15, 14) out of bounds for length 16
Size)andSize(G)<>64 then
 # for these orders the optimal degree is fast enough
 iso:=MinimalFaithfulPermutationRepresentationjava.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 10
 Info(InfoPcGroupreturn Df,
 Size(G),":" );
 returnUserPreference" ijava.lang.StringIndexOutOfBoundsException: Index 65 out of bounds for length 65
 fijava.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5

djava.lang.StringIndexOutOfBoundsException: Range [28, 27) out of bounds for length 31
 if ,j
 # it can -- find a nice decomposition in two

 y;
 java.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 0
 abovent:=function(a Append,\[\";
 local hom,n;
 :=NaturalHomomorphismByNormalSubgroupNC,a);
 b:=Image(hom,b);
 n:)
 =(nx>(,b);
 SortBy(n,x->-
 (hom,x))java.lang.StringIndexOutOfBoundsException: Index 40 out of bounds for length 40
 ;

 java.lang.StringIndexOutOfBoundsException: Range [8, 1) out of bounds for length 19
 if if Size
 d:=[d
,"java.lang.StringIndexOutOfBoundsException: Range [34, 33) out of bounds for length 64
isodxjava.lang.StringIndexOutOfBoundsException: Range [58, 56) out of bounds for length 63
 :=(,x->somorphismPermGroupImagex,));
 ims:=List([1,2],x->List(GeneratorsOfGroup(G),
 y->ImagesRepresentative(d[x],ImagesRepresentative([sPartialPermCollection]coll- (List(coll, ));
 ims:=SubdirectDiagonalPerms(IsPartialPermCollection],coll-UnionList(coll MovedPoints);
 d:=Group([IsPartialPermColl] > ((oll)java.lang.StringIndexOutOfBoundsException: Index 75 out of bounds for length 75
 (, "forpartial "
 s:(, "a permcollection,
 if IsPartialPermCollection List)java.lang.StringIndexOutOfBoundsException: Index 76 out of bounds for length 76
 ims:=List(imsjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 java.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 18
 UseIsomorphismRelation(Gd)
 fi;
 iso:=GroupHomomorphismByImagesNC(G,d,GeneratorsOfGroup(G),ims);
 Assert(1,IsBijective(iso));
 SetIsBijective(iso,true);
 return iso;
 fi;

 p:=Collected(Factors(Size(G)));
 if Length(p)>1 then
 d:=Combinations(p);
 SortBy(d,x->-Product(x,y->y[1]^y[2]));
 for i in d do
 s:=HallSubgroup(G,List(i,x->x[1]));
 if Size(Core(G,s))=1 then
 Info(InfoPcGroup,1,"Hall ",List(i,x->x[1]));

 # try normalizer quotient
 d:=Normalizer(G,s);
 if Size(Core(G,d))=1 then
 s:=d;
 else
 d:=ShallowCopy(IntermediateSubgroups(d,s).subgroups);
 SortBy(d,x->-Size(x));
 a:=First(d,x->Size(Core(G,x))=1);
 if a<>fail then s:=a;fi;
 fi;

 iso:=FactorCosetAction(G,s);
 Assert(1,IsBijective(iso));
 SetIsBijective(iso,true);
 d:=Image(iso);
 UseIsomorphismRelation(G,d);
 return iso;
 fi;
 od;

 else
 # p-group, one minimal: try to go from factor permrep
 d:=MinimalNormalSubgroups(G)[1];
 ims:=NaturalHomomorphismByNormalSubgroupNC(G,d);
 iso:=IsomorphismPermGroup(Image(ims,G));
 ims:=ims*iso;
 a:=Image(ims,G);
 Info(InfoPcGroup,1,"Factor ",List(Orbits(a,MovedPoints(a)),Length));
 s:=List(Orbits(a,MovedPoints(a)),x->Stabilizer(a,x[1]));
 s:=List(s,x->PreImage(ims,x));
 SortBy(s,x->-Size(x));
 for j in [1..Length(Factors(Size(s[1])))] do
 for i in [1..Length(s)] do
 p:=LowLayerSubgroups(s[i],j);
 p:=Filtered(p,x->not IsSubset(x,d));
 if Length(p)>0 then
 d:=Maximum(List(p,Size));
 iso:=FactorCosetAction(G,First(p,x->Size(x)=d));
 ims:=[List(GeneratorsOfGroup(G),x->ImagesRepresentative(iso,x)),
 List(GeneratorsOfGroup(G),x->ImagesRepresentative(ims,x))];
 ims:=SubdirectDiagonalPerms(ims[1],ims[2]);
 d:=Group(ims);
 UseIsomorphismRelation(G,d);
 s:=SmallerDegreePermutationRepresentation(d:cheap);
 if NrMovedPoints(Range(s))<NrMovedPoints(d) then
 ims:=List(ims,x->ImagesRepresentative(s,x));
 d:=Image(s);
 UseIsomorphismRelation(G,d);
 fi;
 iso:=GroupHomomorphismByImagesNC(G,d,GeneratorsOfGroup(G),ims);
 Assert(1,IsBijective(iso));
 SetIsBijective(iso,true);
 return iso;
 fi;
 od;
 od;

 Error("should never happen");
 fi;
end);

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