[GAP Forum] Computing a nonabelian tensor square

[Arturo Magidin]

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