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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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closed as unclear what you're asking by YCor, Igor Belegradek, Benjamin Steinberg, Stefan Kohl, Misha Dec 1 '13 at 22:05

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Out of curiosity, what does it mean for two groups to be quasiisomorphic? –  S. Carnahan Nov 30 '13 at 12:45
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I guess quasiisomorphic should be quasiisometric, right? –  Benoît Kloeckner Nov 30 '13 at 13:29
    
There is a notion of quasi-isomorphic groups but I would bet OP did not mean it. –  Misha Nov 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. –  Misha Nov 30 '13 at 17:11
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What is a bounded group? –  Igor Belegradek Nov 30 '13 at 21:18