Advertisement

Non-amenable finitely presented torsion-by-cyclic groups

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

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.

Keywords

Cyclic Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

Personalised recommendations