[GAP Forum] Computing a nonabelian tensor square

[Luise Kappe]

Arturo,
Your question is completely answered by Theorem 4.4 in the paper
  "Infinite metacyclic groups and their non-abelian tensor squares" by 
J.R.Beuerle and L.-C.Kappe, Proceedings Edinburgh Mathematical Society 
(2000) 43, 651-662.
The non-abelian tensor square of G is isomorphic to
      C_4 x C_2 x C_0 x C_0,
and the non-abelian tensor square of G/Z(G) is isomorphic to
      C_2 x C_2 x C_2 x C_0.
                Hope that helps,
                                  LCK

On Mon, 17 Jun 2013, Arturo Magidin wrote:

> Dear GAP Forum,
>
> I'm not very familiar with the sundry methods for computing the nonabelian 
> tensor square using GAP, or for testing its structural properties. I need a 
> quick computation and I'm hoping someone can point me to the right direction 
> for doing so.
>
> Specifically, I'd like to check the following (full disclosure: it has to do 
> with a paper I'm refereeing):
>
> Let Z be the infinite cyclic group, and let G be the semidirect product of Z 
> with itself, with Z acting nontrivially; that is,
>
> G = < x,y  |   x^y = x^{-1} >
>
> I would like to check whether the nonabelian tensor square of G has torsion, 
> and to confirm that the nonabelian tensor square of G/Z(G) does in fact have 
> torsion. (G/Z(G) is the infinite dihedral group, as Z(G) = <y^2> ).
>
> Thank you,
>
> Arturo
>
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