Geodesic
Non-amenable finitely presented torsion-by-cyclic groups
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
Electronic research announcements of the American Mathematical Society, Tome 07 (2001), pp. 63-71.

Voir la notice de l'article provenant de la source American Mathematical Society

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. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-01-00095-6/

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