Non-amenable finitely presented torsion-by-cyclic groups

  • Alexander Yu. Ol’shanskii
  • Mark V. Sapir

DOI: 10.1007/s10240-002-0006-7

Cite this article as:
Ol’shanskii, A. & Sapir, M. Publ. math., Inst. Hautes Étud. Sci. (2003) 96: 43. doi:10.1007/s10240-002-0006-7

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.

Copyright information

© Institut des Hautes Études Scientifiques et Springer-Verlag Berlin Heidelberg, 2003

Authors and Affiliations

  • Alexander Yu. Ol’shanskii
    • 1
  • Mark V. Sapir
    • 2
  1. 1.Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, TN 37240, USA, alexander.olshanskiy@vanderbilt.edu, http://www.math.vanderbilt.edu/∼olsh and Department of Higher Algebra, MEHMAT, Moscow State University, Moscow, Russia, olshan@shabol.math.msu.suUS
  2. 2.Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, TN 37240, USA, http://www.math.vanderbilt.edu/∼msapirUS

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