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#############################################################################
##
#W grppcprp.gi GAP Library Frank Celler
#W & Bettina Eick
##
#H @(#)$Id: grppcprp.gi,v 4.6 2002/04/15 10:04:52 sal Exp $
##
#Y Copyright (C) 1996, 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
##
## This file contains the methods for properties of polycylic groups.
##
Revision.grppcprp_gi :=
"@(#)$Id: grppcprp.gi,v 4.6 2002/04/15 10:04:52 sal Exp $";
InstallMethod( IsNilpotentGroup,
"method for pc groups",
true,
[IsGroup and CanEasilyComputePcgs],
0,
function( G )
local w;
w := LGWeights( SpecialPcgs(G) );
return w[Length(w)][1] = 1;
end);
InstallMethod( IsSupersolvableGroup,
"method for pc groups",
true,
[IsGroup and CanEasilyComputePcgs],
0,
function( G )
local pr, spec, pcgs, p, sub, fac, mats, modu, facs;
pr := Set(FactorsInt(Size(G)));
spec := SpecialPcgs(G);
pcgs := InducedPcgs( spec, FrattiniSubgroup( G ) );
for p in pr do
sub := InducedPcgsByPcSequenceAndGenerators( spec, pcgs,
GeneratorsOfGroup( PCore(G, p) ) );
if Length(sub) > Length(pcgs) then
fac := sub mod pcgs;
mats := LinearOperationLayer( G, fac );
modu := GModuleByMats( mats, GF(p) );
facs := MTX.CompositionFactors( modu );
if not ForAll( facs, x -> x.dimension = 1 ) then
return false;
fi;
fi;
od;
return true;
end);
#############################################################################
##
#E grppcpprp.gi . . . . . . . . . . . . . . . . . . . . . . . . . ends here
##
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