Geodesic
Complementing a subgroup of a hyperbolic group by a free factor
Algebra i logika, Tome 52 (2013) no. 3, pp. 332-351

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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. 
@article{AL_2013_52_3_a3,
     author = {F. A. Dudkin and K. S. Sviridov},
     title = {Complementing a~subgroup of a~hyperbolic group by a~free factor},
     journal = {Algebra i logika},
     pages = {332--351},
     publisher = {mathdoc},
     volume = {52},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2013_52_3_a3/}
}
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F. A. Dudkin; K. S. Sviridov. Complementing a subgroup of a hyperbolic group by a free factor. Algebra i logika, Tome 52 (2013) no. 3, pp. 332-351. http://geodesic.mathdoc.fr/item/AL_2013_52_3_a3/