Geodesic
Non-amenable finitely presented torsion-by-cyclic groups
Ol’shanskii, A.1 ; Sapir, M.2
1Department of Mathematics, Vanderbilt University, Nashville, TN 37240, and Department of Mechanics and Mathematics, Moscow State University, Moscow, Russia
2Department of Mathematics, Vanderbilt University, Nashville, TN 37240
Electronic research announcements of the American Mathematical Society, Tome 07 (2001), pp. 63-71
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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 $[x,y]^n=1$.
DOI : 10.1090/S1079-6762-01-00095-6

Ol’shanskii, A.  1   ; Sapir, M.  2

1 Department of Mathematics, Vanderbilt University, Nashville, TN 37240, and Department of Mechanics and Mathematics, Moscow State University, Moscow, Russia
2 Department of Mathematics, Vanderbilt University, Nashville, TN 37240 
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Ol’shanskii, A.; Sapir, M. Non-amenable finitely presented torsion-by-cyclic groups. Electronic research announcements of the American Mathematical Society, Tome 07 (2001), pp. 63-71. doi: 10.1090/S1079-6762-01-00095-6

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