Non-amenable finitely presented torsion-by-cyclic groups


We construct a finitely presented non-amenable group without free non-cyclic subgroups thus providing a finitely presented counterexample to von Neumann’s problem. Our group is an extension of a group of finite exponent n >> 1 by a cyclic group, so it satisfies the identity [x, y] = 1. 

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@inproceedings{Olshanskii2001NonamenableFP, title={Non-amenable finitely presented torsion-by-cyclic groups}, author={A. S. Ol’shanskii and Marina Sapir}, year={2001} }