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#############################################################################
##
#W grppcext.gd GAP library Bettina Eick
##
#Y Copyright (C) 1997, Lehrstuhl D fuer Mathematik, RWTH Aachen, Germany
#Y (C) 1998 School Math and Comp. Sci., University of St. Andrews, Scotland
#Y Copyright (C) 2002 The GAP Group
##
Revision.grppcext_gd :=
"@(#)$Id: grppcext.gd,v 4.19 2002/04/15 10:04:51 sal Exp $";
#############################################################################
##
#I InfoCompPairs
#I InfoExtReps
##
DeclareInfoClass( "InfoCompPairs" );
DeclareInfoClass( "InfoExtReps");
#############################################################################
##
#F MappedPcElement( <elm>, <pcgs>, <list> )
##
## returns the image of <elm> when mapping the pcgs <pcgs> onto <list>
## homomorphically.
DeclareGlobalFunction("MappedPcElement");
#############################################################################
##
#F ExtensionSQ( <C>, <G>, <M>, <c> )
##
DeclareGlobalFunction( "ExtensionSQ" );
#############################################################################
##
#F FpGroupPcGroupSQ( <G> )
##
DeclareGlobalFunction( "FpGroupPcGroupSQ" );
#############################################################################
##
#F CompatiblePairs( <G>, <M> [,<D>] )
##
## returns the group of compatible pairs of the group <G> with the
## <G>-module <M> as subgroup of the direct product of <Aut(G)> x <Aut(M)>.
## Here <Aut(M)> is considered as subgroup of a general linear group. The
## optional argument <D> should be a subgroup of <Aut(G)> x <Aut(M)>. If it
## is given, then only the compatible pairs in <D> are computed.
DeclareGlobalFunction( "CompatiblePairs" );
#############################################################################
##
#O Extension( <G>, <M>, <c> )
#O ExtensionNC( <G>, <M>, <c> )
##
## returns the extension of <G> by the <G>-module <M> via the cocycle <c>
## as pc groups. The `NC' version does not check the resulting group for
## consistence.
DeclareOperation( "Extension", [ CanEasilyComputePcgs, IsObject, IsVector ] );
DeclareOperation( "ExtensionNC", [ CanEasilyComputePcgs, IsObject, IsVector ] );
#############################################################################
##
#O Extensions( <G>, <M> )
##
## returns all extensions of <G> by the <G>-module <M> up to equivalence
## as pc groups.
DeclareOperation( "Extensions", [ CanEasilyComputePcgs, IsObject ] );
#############################################################################
##
#O ExtensionRepresentatives( <G>, <M>, <P> )
##
## returns all extensions of <G> by the <G>-module <M> up to equivalence
## under action of <P> where <P> has to be a subgroup of the group of
## compatible pairs of <G> with <M>.
DeclareOperation( "ExtensionRepresentatives",
[CanEasilyComputePcgs, IsObject, IsObject] );
#############################################################################
##
#O SplitExtension( <G>, <M> )
#O SplitExtension( <G>, <aut>, <N> )
##
## returns the split extension of <G> by the <G>-module <M>. In the second
## form it returns the split extension of <G> by the arbitrary finite group
## <N> where <aut> is a homomorphism of <G> into Aut(<N>).
DeclareOperation( "SplitExtension", [CanEasilyComputePcgs, IsObject] );
#############################################################################
##
#O TopExtensionsByAutomorphism( <G>, <aut>, <p> )
##
DeclareOperation( "TopExtensionsByAutomorphism",
[CanEasilyComputePcgs, IsObject, IsInt] );
#############################################################################
##
#O CyclicTopExtensions( <G>, <p> )
##
DeclareOperation( "CyclicTopExtensions",
[CanEasilyComputePcgs, IsInt] );
#############################################################################
##
#A SocleComplement(<G>)
##
DeclareAttribute( "SocleComplement", IsGroup );
#############################################################################
##
#A SocleDimensions(<G>)
##
DeclareAttribute( "SocleDimensions", IsGroup );
#############################################################################
##
#A ModuleOfExtension( < G > );
##
DeclareAttribute( "ModuleOfExtension", IsGroup );
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