[GAP Forum] A possibly wrong output in MeatAxe

[Alexander Hulpke]

Dear Forum,

``Anvita'' wrote:
> I am suspecting that GAP's function for finding composition factors
> of a MeatAxe module could be producing an incorrect answer in the
> following example which counts the multiplicities of composition factors
> of the regular module for A_5 over its splitting field GF(4).

No, what is happening in the calculation is that you don't construct the regular action, but the conjugation action of A on itself. (The default action is `OnPoints' which corresponds to the ^ operator.)
> 
> A:=AlternatingGroup(5);
> G:=Action(A,A);
If you use
GG:=Action(A,A,OnRight);

> gg:=GeneratorsOfGroup(GG);
> reg:=List(gg,g->PermutationMat(g,60,GF(4)));
> M:=GModuleByMats(reg,GF(4));
> com:=MTX.CollectedFactors(M);;
> List(com,t->[MTX.Dimension(t[1]),t[2]]);

you get dimensions
[ [ 1, 12 ], [ 2, 8 ], [ 2, 8 ], [ 4, 4 ] ]
which I believe agrees with what some other system calculates.

Regards,

   Alexander Hulpke