This [question][1] was answered by @Jim Belk And he defined $G_n$ as follows:
$$
G_n \;=\; \langle a,b \mid [a^{-1}ba,b] = \cdots = [a^{-n}ba^n,b]=1\rangle
$$
My question is:  
Are $G_n$'s mutually non-isomorphic? (i.e., for every two distinct natural numbers $n$ and $m$, $G_n$ and $G_m$ are not isomorphic).  
 
Could you please help me to find my answer.

Thanks,








[1]:https://math.stackexchange.com/questions/547087/finitely-generated-group-which-is-not-finitely-presented/547144#comment4975221_547144