This article is cited in 1 paper

Complementing a subgroup of a hyperbolic group by a free factor

F. A. Dudkin^ab, K. S. Sviridov<sup>c

a</sup> Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia
^b Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia
^c Morskoi pr. 29-9, Novosibirsk, 630090, Russia

Abstract: Let $G$ be a hyperbolic group that is not almost cyclic and $H$ be its quasiconvex subgroup of infinite index. We find necessary and sufficient conditions of there being for $H$ a free subgroup $F$ of rank 2 in $G$ such that $F$ and $H$ generate a free product $F*H\subseteq G$. It is proved that $F*H$ is quasiconvex and that there exists an algorithm for verifying the conditions of the criterium given $G$ and $H$.

Keywords: hyperbolic group, quasiconvex subgroup, free product.

UDC: 512.543

Received: 03.02.2012
Revised: 13.03.2013

 English version: Algebra and Logic, 2013, 52:3, 222–235

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