Non-amenable finitely presented torsion-by-cyclic groups

2003/05/07 by Alexander Olshanskii, Mark Sapir · 2 citations
Mathematics · Computer Science · #Geometric and Algebraic Topology #semigroups and automata theory #Mathematical Dynamics and Fractals #Counterexample #Finitely-generated abelian group #Mathematics #Torsion (gastropod) #Stallings theorem about ends of groups #Cyclic group #Exponent #Pure mathematics #Amenable group #Finitely generated group #Von Neumann architecture #Group (periodic table) #Locally finite group #Combinatorics #Discrete mathematics #Physics

paper · pdf · doi:10.1007/s10240-002-0006-7

openalex publication_date 2003/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/23

Abstract

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.

Citations

• Zur allgemeinen Theorie des Masses
• Sur la décomposition des ensembles de points en parties respectivement congruentes
• Groups of piecewise linear homeomorphisms of the real line
• Free subgroups in linear groups
• On groups with full Banach mean value

Cited by

• ELEMENTARY AMENABLE SUBGROUPS OF R. THOMPSON'S GROUP F
• Amenable group [wikipedia]