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#############################################################################
##
## This file is part of GAP, a system for computational discrete algebra.
## This file's authors include Frank Celler, Alexander Hulpke.
##
## 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 operations for the computation of complements in
## pc groups
##
#############################################################################
##
#V InfoComplement
##
## <#GAPDoc Label="InfoComplement">
## <ManSection>
## <InfoClass Name="InfoComplement"/>
##
## <Description>
## Info class for the complement routines.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareInfoClass("InfoComplement");
#############################################################################
##
#F COAffineBlocks( <S>,<Sgens>,<mats>,<orbs> )
##
## <ManSection>
## <Func Name="COAffineBlocks" Arg='S,Sgens,mats,orbs'/>
##
## <Description>
## Let <A>S</A> be a group whose generators <A>Sgens</A> act via <A>mats</A> on an affine
## space. This routine calculates the orbits under this action. If <A>orbs</A>
## also orbits as sets of vectors are returned.
## </Description>
## </ManSection>
##
DeclareGlobalFunction("COAffineBlocks");
#############################################################################
##
#O CONextCentralizer( <ocr>, <S>, <H> ) . . . . . . . . . . . . . . . local
##
## <ManSection>
## <Oper Name="CONextCentralizer" Arg='ocr, S, H'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareGlobalFunction("CONextCentralizer");
#############################################################################
##
#O COAffineCohomologyAction( <ocr>, <fgens>, <acts>,<B> )
##
## <ManSection>
## <Oper Name="COAffineCohomologyAction" Arg='ocr, fgens, acts,B'/>
##
## <Description>
## calculates matrices for the affine action of a factor centralizer on the
## complements, represented by elements of the cohomology group. <A>B</A> is the
## result of <C>BaseSteinitzVectors</C> used to represent the cohomology group.
## </Description>
## </ManSection>
##
DeclareGlobalFunction("COAffineCohomologyAction");
#############################################################################
##
#O CONextCocycles( <cor>, <ocr>, <S> ) . . . . . . . . . . . . . . . . local
##
## <ManSection>
## <Oper Name="CONextCocycles" Arg='cor, ocr, S'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareGlobalFunction("CONextCocycles");
#############################################################################
##
#O CONextCentral( <cor>, <ocr>, <S> ) . . . . . . . . . . . . . . . . local
##
## <ManSection>
## <Oper Name="CONextCentral" Arg='cor, ocr, S'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareGlobalFunction("CONextCentral");
#############################################################################
##
#O CONextComplements( <cor>, <S>, <K>, <M> ) . . . . . . . . . . . . . local
##
## <ManSection>
## <Oper Name="CONextComplements" Arg='cor, S, K, M'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareGlobalFunction("CONextComplements");
#############################################################################
##
#O COComplements( <cor>, <G>, <N>, <all> ) . . . . . . . . . . . . . . local
##
## <ManSection>
## <Oper Name="COComplements" Arg='cor, G, N, all'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareGlobalFunction("COComplements");
#############################################################################
##
#O COComplementsMain( <G>, <N>, <all>, <fun> ) . . . . . . . . . . . . . local
##
## <ManSection>
## <Oper Name="COComplementsMain" Arg='G, N, all, fun'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareGlobalFunction("COComplementsMain");
#############################################################################
##
#O ComplementClassesRepresentativesSolvableNC( <G>, <N> )
##
## <ManSection>
## <Oper Name="ComplementClassesRepresentativesSolvableNC" Arg='G, N'/>
##
## <Description>
## computes a set of representatives of the complement classes of <A>N</A> in
## <A>G</A> by cohomological methods. <A>N</A> must be a solvable normal subgroup
## of <A>G</A>.
## </Description>
## </ManSection>
##
DeclareOperation("ComplementClassesRepresentativesSolvableNC",
[IsGroup,IsGroup]);
# Basic routine for complements with solvable factor group.
DeclareGlobalFunction("COSolvableFactor");
#############################################################################
##
#O ComplementClassesRepresentatives( <G>, <N> ) . . . . . . . . . . . . find all complement
##
## <#GAPDoc Label="ComplementClassesRepresentatives">
## <ManSection>
## <Oper Name="ComplementClassesRepresentatives" Arg='G, N'/>
##
## <Description>
## Let <A>N</A> be a normal subgroup of <A>G</A>.
## This command returns a set of representatives for the conjugacy classes
## of complements of <A>N</A> in <A>G</A>.
## Complements are subgroups of <A>G</A> which intersect trivially with
## <A>N</A> and together with <A>N</A> generate <A>G</A>.
## <P/>
## At the moment methods are available only for the case that <A>N</A> or
## <A>G</A><C>/</C><A>N</A> is solvable.
## <Example><![CDATA[
## gap> ComplementClassesRepresentatives(g,Group((1,2)(3,4),(1,3)(2,4)));
## [ Group([ (3,4), (2,4,3) ]) ]
## ]]></Example>
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareOperation("ComplementClassesRepresentatives",[IsGroup,IsGroup]);
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