[GAP Forum] The function DirectProduct

[Ramon Esteban-Romero]

Dear forum,

It seems that in the first case, the function constructs a permutation
group because S was a permutation group. Hence it is possible to
compare both groups as, for example, subgroups of a permutation
group. In the second case, it seems that G is constructed as a new pc
group, and since it is constructed as a new group, it is not
comparable with the old one.

In the second case you can use the group homomorphism Embedding(g,1)
to identify C with G (or, in general, with the corresponding subgroup
of G).

Best wishes,
-- 
Ramon <resteban at mat.upv.es>

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* Luyện Lê Văn <lvluyen at gmail.com> [111214 19:47]:
> Dear forum,
> 
> When I ran the below code lines:
> gap >S:=SymmetricGroup(3);;
> gap >G:=DirectProduct(S);;
> gap >G=S;
>         true
> 
> gap >C:=CyclicGroup(3);;
> gap >G:=DirectProduct(C);;
> gap >G=C;
>         false
> 
> I realized that there was a difference when I used SymmetricGroup and
> CyclicGroup. Could you explain it?
> 
> Thanks,
> 
> Luyen.
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