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BindGlobal( "HaveIsomorphicModularGroupAlgebras", function(G, H)
local p, TG, TH, CG, CH;
if Size(G) <> Size(H) then return false; fi;
if RankPGroup(G) <> RankPGroup(H) then return false; fi;
p := PrimePGroup(G);
TG := TableByWeightedBasisOfRad( GroupRing(GF(p), G ) );
TH := TableByWeightedBasisOfRad( GroupRing(GF(p), H ) );
if TG.wgs <> TH.wgs then return false; fi;
if CompareTables(TG, TH) then return true; fi;
CG := CanoFormWithAutGroupOfTable(TG).cano;
CH := CanoFormWithAutGroupOfTable(TH).cano;
return CompareTables(CG, CH);
end );
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