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#############################################################################
##
#W ctblpc.gi GAP library Alexander Hulpke
##
#H @(#)$Id: ctblpc.gi,v 4.8 2002/04/15 10:04:35 sal Exp $
##
#Y Copyright (C) 1993, 1997
#Y (C) 1998 School Math and Comp. Sci., University of St. Andrews, Scotland
#Y Copyright (C) 2002 The GAP Group
##
## This file contains the parts of the Dixon-Schneider specific to pc groups
##
Revision.ctblpc_gi :=
"@(#)$Id: ctblpc.gi,v 4.8 2002/04/15 10:04:35 sal Exp $";
#############################################################################
##
#F PcGroupClassMatrixColumn(<D>,<mat>,<r>,<t>) . calculate the t-th column
#F of the r-th class matrix and store it in the appropriate column of M
##
PcGroupClassMatrixColumn := function(D,M,r,t)
local c,s,z,i,T,p,orb;
if t=1 then
M[D.inversemap[r]][t]:=D.classiz[r];
else
orb:=DxGaloisOrbits(D,r);
z:=D.classreps[t];
c:=orb.orbits[t][1];
if c<>t then
p:=RepresentativeAction(orb.group,c,t);
# was the first column of the galois class active?
if ForAny(M,i->i[c]>0) then
for i in D.classrange do
M[i^p][t]:=M[i][c];
od;
Info(InfoCharacterTable,2,"by GaloisImage");
return;
fi;
fi;
T:=DoubleCentralizerOrbit(D,r,t);
Info(InfoCharacterTable,2,Length(T[1])," instead of ",D.classiz[r]);
for i in [1..Length(T[1])] do
T[1][i]:=T[1][i]*z;
od;
#T AH: Here something goes wrong in the solvable group class
#T computation. Workaround
T[1]:=List(T[1],i->Position(D.ids,D.identification(D,i)));
#T[1]:=List(ClassesSolvableGroup(D.group,0,rec(candidates:=T[1])),
# i->Position(D.ids,i.representative));
for i in [1..Length(T[1])] do
s:=T[1][i];
M[s][t]:=M[s][t]+T[2][i];
od;
fi;
end;
#############################################################################
##
#F IdentificationSolvableGroup(<D>,<el>) . . class invariants for el in G
##
IdentificationSolvableGroup := function(D,el)
return ClassesSolvableGroup(D.group,0,rec(candidates:=[el]))[1].representative;
end;
#############################################################################
##
#M DxPreparation(<G>)
##
InstallMethod(DxPreparation,"pc group",true,[IsPcGroup,IsRecord],0,
function(G,D)
local i,cl;
if not IsDxLargeGroup(G) then
TryNextMethod();
fi;
D.ClassElement:=ClassElementLargeGroup;
D.identification:=IdentificationSolvableGroup;
D.rationalidentification:=IdentificationGenericGroup;
D.ClassMatrixColumn:=PcGroupClassMatrixColumn;
cl:=D.classes;
D.ids:=[];
D.rids:=[];
for i in D.classrange do
D.ids[i]:=D.identification(D,D.classreps[i]);
D.rids[i]:=D.rationalidentification(D,D.classreps[i]);
od;
return D;
end);
#############################################################################
##
#E ctblpc.gi
##
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