[GAP Forum] Bug in SemidirectProduct?

[Alexander Hulpke]

Dear Forum, Dear Benjamin Sambale,
>
> G:=AlternatingGroup(4);
> N:=Subgroup(G,[(1,2)(3,4),(1,3)(2,4)]);
> H:=DirectProduct(CyclicGroup(2),CyclicGroup(2));
> A:=AutomorphismGroup(H);
> P:=SylowSubgroup(A,3);
> epi:=NaturalHomomorphismByNormalSubgroup(G,N);
> iso:=IsomorphismGroups(FactorGroup(G,N),P);
> f:=CompositionMapping(IsomorphismGroups(FactorGroup(G,N),P),epi);
> SemidirectProduct(G,f,H);
>
> After the command "SemidirectProduct(G,f,H);" GAP returns:
>
> "Error, not ready yet, only finite polycyclic groups are allowed"
>
> But every group in my example is finite polycyclic, even the  
> semidirect product would be. I can't imagine, what should be the  
> problem in constructing semidirect products.

The problem is that G is not a PC group and the method for PC groups  
claims to apply (because G is solvable), but the presentation GAP  
finds for G (likely looked up, as the group is alternating) is not a  
pc presentation.

This will be fixed in the next bugfix (the method should not apply,  
there is a fallback method that does conversion of the  
representation), in the meantime a workaround would be to convert both  
groups (G and H) into permutation groups (or -- if solvable -- pc  
groups).

Best wishes,

     Alexander Hulpke




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