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## radical.gd CRISP Burkhard Höfling
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## Copyright © 2000, 2002 Burkhard Höfling
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#A Radical(<grp>, <class>)
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## this is defined for arbitrary classes to allow radicals wrt. Fitting sets
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KeyDependentOperation("Radical", IsGroup, IsClass, ReturnTrue);
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#O OneInvariantSubgroupMaxWrtNProperty(<act>, <grp>, <pretest>, <test>, <data>)
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## See the manual.
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DeclareOperation("OneInvariantSubgroupMaxWrtNProperty",
[IsListOrCollection, IsGroup, IsFunction, IsFunction, IsObject]);
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#O AllInvariantSubgroupsWithNProperty(<act>, <grp>, <pretest>, <test>, <data>)
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## See the manual.
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DeclareOperation("AllInvariantSubgroupsWithNProperty",
[IsListOrCollection, IsGroup, IsFunction, IsFunction, IsObject]);
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#O OneNormalSubgroupMaxWrtNProperty(<act>, <grp>, <pretest>, <test>, <data>)
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## See the manual.
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DeclareOperation("OneNormalSubgroupMaxWrtNProperty",
[IsGroup, IsFunction, IsFunction, IsObject]);
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#O AllNormalSubgroupsWithNProperty(<grp>, <pretest>, <test>, <data>)
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## See the manual.
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DeclareOperation("AllNormalSubgroupsWithNProperty",
[IsGroup, IsFunction, IsFunction, IsObject]);
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#F InvariantSubgroupsCA(
#F act, ser, avoid, cover, property, max) . . . local
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## ser must be a series invariant under act, and act must generate the full
## inner automorphism group on ser[1].
## if all is true, InvariantSubgroupsCA computes the act-invariant
## subgroups N of ser[1] such that ser[cover] equals the intersection of N
## and ser[avoid], N contains ser[cover] properly, and property(N) returns
## true.
## If all is false, InvariantSubgroupsCA only returns the
## subgroups N
## which are maximal subject to the above conditions. property must be
## inherited by act-invariant subgroups, and property(ser[cover])
## is assumed to be true
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DeclareGlobalFunction("InvariantSubgroupsCA");
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#E
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