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

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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