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Non-amenable finitely presented torsion-by-cyclic groups


Authors: A. Yu. Ol'shanskii and M. V. Sapir
Journal: Electron. Res. Announc. Amer. Math. Soc. 7 (2001), 63-71
MSC (2000): Primary 20F05, 43A07
DOI: https://doi.org/10.1090/S1079-6762-01-00095-6
Published electronically: July 3, 2001
MathSciNet review: 1852901
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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 $n\gg 1$ by a cyclic group, so it satisfies the identity $[x,y]^n=1$.


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Additional Information

A. Yu. Ol'shanskii
Affiliation: Department of Mathematics, Vanderbilt University, Nashville, TN 37240, and Department of Mechanics and Mathematics, Moscow State University, Moscow, Russia
Email: olsh@math.vanderbilt.edu, olshan@shabol.math.msu.su

M. V. Sapir
Affiliation: Department of Mathematics, Vanderbilt University, Nashville, TN 37240
Email: msapir@math.vanderbilt.edu

DOI: https://doi.org/10.1090/S1079-6762-01-00095-6
Keywords: Amenable group, Burnside groups, free subgroups
Received by editor(s): January 9, 2001
Published electronically: July 3, 2001
Additional Notes: Both authors were supported in part by the NSF grant DMS 0072307. In addition, the research of the first author was supported in part by the Russian fund for fundamental research 99-01-00894, and the research of the second author was supported in part by the NSF grant DMS 9978802.
Communicated by: Efim Zelmanov
Article copyright: © Copyright 2001 American Mathematical Society

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