[GAP Forum] Presentation

[Hebert Pérez-Rosés]

Dear Abdulsatar,

I do not quite understand your question. I suppose that you want to
know whether the two groups specified by both presentations are
isomorphic. But you say that both presentations are of the same group,
namely the automorphism group of the free Abelian group of rank n. If
that is so, then obviously both groups are isomorphic, since they are
the same group !!

On the other hand, if you want to know, for two arbitrary
presentations P_1 and P_2, whether the corresponding groups G_1 and
G_2 are isomorphic, then it is impossible in general. This is one of
the three problems stated by Max Dehn in 1911, which turned out to be
unsolvable. The other two are the word problem and the conjugacy
problem. It is possible, however, to solve the problem for some
special  classes of presentations.

I hope this answers your questions.

Best regards,

Hebert Perez-Roses
The University of Lleida, Spain




2013/2/25 Abdulsatar Al-Juburie <a.j.t.al-juburie at newcastle.ac.uk>:
> Dear Forum,
>
>  I got by using GAP two  presentations for the automorphism of group of the free Abelian group of rank n. . However, I ask  if there is any way in GAP to let me know if these two presentations are isomorphic.
>
> I would be appreciated if you could help me in this matter.
>
> Best Regards,
>
> Abdulsatar
>
>
>
>
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