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Non-amenable finitely presented torsion-by-cyclic groups

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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 ≫ 1 by a cyclic group, so it satisfies the identity [x,y]n = 1.

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Authors and Affiliations

  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.su, , , , , , US

    Alexander Yu. Ol’shanskii

  2. Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, TN 37240, USA, http://www.math.vanderbilt.edu/∼msapir, , , , , , US

    Mark V. Sapir

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  1. Alexander Yu. Ol’shanskii
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  2. Mark V. Sapir
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Manuscrit reĉu le 8 février 2001.

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ID="*"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 Basic Research 99-01-00894 and by the INTAS grant, the research of the second author was supported in part by the NSF grant DMS 9978802.

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Ol’shanskii, A., Sapir, M. Non-amenable finitely presented torsion-by-cyclic groups. Publ. math., Inst. Hautes Étud. Sci. 96, 43–169 (2003). https://doi.org/10.1007/s10240-002-0006-7

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  • DOI: https://doi.org/10.1007/s10240-002-0006-7

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