MATHEMATICS

Finite generated subgroups of hyperbolic groups

A. P. Goryushkin

Vitus Bering Kamchatka State University, 683031, Petropavlovsk-Kamchatsky, Pogranichnaya st., 4, Russia

Abstract: It is proved that finite generated subgroups of infinite index of hyperbolic groups which are not quasi Abelian are complemented with a nontrivial free factor.

Keywords: hyperbolic group, free product, free product with amalgamation, set of generators, index of a subgroup, normal subgroup.

UDC: 512.24

MSC: 18A32

Received: 02.09.2014

DOI: 10.18454/2079-6641-2014-9-2-7-10

 English version: Bulletin KRASEC. Physical and Mathematical Sciences, 2014, 9:2, 23–26

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