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 <reste...@mat.upv.es>
Clau pública PGP/Llave pública PGP/Clef publique PGP/PGP public key:
http://www.rediris.es/cert/servicios/keyserver/
http://personales.upv.es/~resteban/resteban.asc
Telèfon/teléfono/téléphone/phone: (+34)963877007 ext. 76676
* Luyện Lê Văn <lvlu...@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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