Non-amenable finitely presented torsion-by-cyclic groups

2002/08/30 by A. Yu. Olshanskii, Olshanskii, A. Yu., M. V. Sapir +1 · 1 citation
Mathematics · #20F05 #20F50 #20F65 #FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR) #math.FA #math.GR #msc:20F05 #msc:20F50 #msc:20F65

paper · pdf · doi:10.48550/arxiv.math/0208237

arxiv created 2002/08/30 · arxiv updated 2009/11/30

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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