Quelle  gp2ind.gd   Sprache: Shell

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#W  gp2ind.gd                   GAP4 package `XMod'             Chris Wensley
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#Y  Copyright (C) 2001-2024, Chris Wensley et al,  
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##  This file declares functions for induced crossed modules. 
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##  Layout of groups for induced crossed module calculations:
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##          Fin. Pres. Groups              Groups
##          =================           ============
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##        FN=FM -------> FI            N=M -------> I
##            |          |              |           |
##            |          |              |           |
##            V          V              V           V
##           FP -------> FQ             P --------> Q
##
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##  Layout of groups for induced cat1-group calculations:
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##                                          iota*
##         G ------------> I         PG ------------> PI
##         ||             ||         ||               || 
##         ||             ||         ||               ||  
##         th            t*h*        th              t*h* 
##         ||             ||         ||               || 
##         ||             ||         ||               || 
##         VV             VV         VV               VV 
##         R ------------> Q         PR ------------> PQ
##                                          iota
##
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#A  InducedXModData( <IX> )
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##  DeclareAttribute( "InducedXModData", Is2DimensionalDomain, "mutable" );

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#O  CoproductXMod( <xmod>, <xmod> )
#A  CoproductInfo( <xmod> ) 
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DeclareOperation( "CoproductXMod", [ IsXMod, IsXMod ] ); 
DeclareOperation( "CoproductXMod", [ IsList ] ); 
DeclareAttribute( "CoproductInfo", IsXMod, "mutable" );

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#P  IsInducedXMod( <IX> )
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DeclareProperty( "IsInducedXMod", IsXMod );

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#A  MorphismOfInducedXMod( <IX> )
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DeclareAttribute( "MorphismOfInducedXMod", IsInducedXMod );

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#F  InducedXMod( <args> )
#O  InducedXModBySurjection( <xmod>, <hom> )
#O  InducedXModByCoproduct( <xmod>, <hom> )
#O  InducedXModByBijection( <xmod>, <hom> )
#O  InducedXModByCopower( <grp>, <hom>, <trans> )
#O  InducedXModFromTrivialSource( <xmod>, <hom> )
#O  InducedXModFromTrivialRange( <xmod>, <hom> )
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DeclareGlobalFunction( "InducedXMod" );
DeclareOperation( "InducedXModBySurjection", 
    [ IsXMod, IsGroupHomomorphism ] );
DeclareOperation( "InducedXModByCoproduct", 
    [ IsXMod, IsGroupHomomorphism ] );
DeclareOperation( "InducedXModByBijection", 
    [ IsXMod, IsGroupHomomorphism ] );
DeclareOperation( "InducedXModByCopower", 
    [ IsXMod, IsGroupHomomorphism, IsList ] );
DeclareOperation( "InducedXModFromTrivialSource", 
    [ IsXMod, IsGroupHomomorphism ] );
DeclareOperation( "InducedXModFromTrivialRange", 
    [ IsXMod, IsGroupHomomorphism ] );

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#F  InducedCat1Group( <args> )
#O  InducedCat1Data( <grp>, <hom>, <trans> )
#O  InducedCat1GroupByFreeProduct( [ <grp>, <hom> ] )  ???
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DeclareGlobalFunction( "InducedCat1Group" );
DeclareOperation( "InducedCat1Data", 
    [ IsCat1Group, IsGroupHomomorphism, IsList ] );
DeclareOperation( "InducedCat1GroupByFreeProduct", [ IsList ] );

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#O  AllInducedXMods( <grp> )
#O  AllInducedCat1Groups( <grp> )
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DeclareGlobalFunction( "AllInducedXMods" );
DeclareGlobalFunction( "AllInducedCat1Groups" );