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#W  grppcprp.gi                 GAP Library                      Frank Celler
#W                                                             & Bettina Eick
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#Y  Copyright (C)  1996,  Lehrstuhl D für Mathematik,  RWTH Aachen,  Germany
#Y  (C) 1998 School Math and Comp. Sci., University of St Andrews, Scotland
#Y  Copyright (C) 2002 The GAP Group
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##  This file contains the methods for properties of polycylic groups.
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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 := PrimeDivisors(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);

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#E  grppcpprp.gi  . . . . . . . . . . . . . . . . . . . . . . . . . ends here
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