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TestRandomIrreducibleSolvableMatrixGroup := function (n, q, d, k, e)
local x, y, G, repG, H1, H, gens, M, rep, info;
G := IrreducibleSolvableMatrixGroup (n, q, d, k);
repG := RepresentationIsomorphism (G);
H1 := Source (repG);
H := TrivialSubgroup (H1);
gens := [];
while Size (H) < Size (H1) do
x := Random (H1);
if not x in H then
H := ClosureSubgroupNC (H, x);
Add (gens, x);
fi;
od;
y := RandomInvertibleMat (n, GF(q^e));
M := GroupWithGenerators (List (gens, x -> ImageElm (repG, x)^y));
SetSize (M, Size (G));
SetIsSolvableGroup (M, true);
SetIdIrreducibleSolvableMatrixGroup (M, IdIrreducibleSolvableMatrixGroup (G));
rep := GroupGeneralMappingByImagesNC (H1, M, gens, GeneratorsOfGroup (M));
SetIsGroupHomomorphism (rep, true);
SetIsSingleValued (rep, true);
SetIsBijective (rep, true);
SetRepresentationIsomorphism (M, rep);
info := RecognitionIrreducibleSolvableMatrixGroup (M, true, true, true);
if info.id <> [n, q, d, k] then;
Error("wrong id ", info, ", expected ", [n, q, d, k]);
fi;
if ForAny (GeneratorsOfGroup (Source (rep)),
g -> ImageElm (rep, g) ^info.mat
<> ImageElm (RepresentationIsomorphism(info.group), ImageElm (info.iso, g))) then
Error ("wrong conjugating matrix");
fi;
end;
[ Dauer der Verarbeitung: 0.37 Sekunden
(vorverarbeitet)
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