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Non-amenable finitely presented torsion-by-cyclic groups

A. Yu. Olshanskii·M. V. Sapir
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Abstract

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]^n = 1.

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A. Yu. Olshanskii, M. V. Sapir. 2002-08-30. Non-amenable finitely presented torsion-by-cyclic groups. https://arxiv.org/abs/math/0208237

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