Are there two finitely generated quasiisomorphic groups $G$ and $H$ such that $G$ is torsionfree and $H$ has torsion elements of arbitrarily large order?

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question.If this question can be reworded to fit the rules in the help center, please edit the question.

4

Out of curiosity, what does it mean for two groups to be quasiisomorphic?
– S. Carnahan♦Nov 30 '13 at 12:45

2

I guess quasiisomorphic should be quasiisometric, right?
– Benoît KloecknerNov 30 '13 at 13:29

There is a notion of quasi-isomorphic groups but I would bet OP did not mean it.
– MishaNov 30 '13 at 15:55

The groups to check would be Tarski monsters with infinite central normal subgroup: is the extension class bounded or not. In the former case you get an example.
– MishaNov 30 '13 at 17:11

3

What is a bounded group?
– Igor BelegradekNov 30 '13 at 21:18