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 ⊆ G. It is proved that F ∗H is quasiconvex and that there exists an algorithm for verifying the conditions of the criterion given G and H.
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Translated from Algebra i Logika, Vol. 52, No. 3, pp. 332-351, May-June, 2013.
*Supported by RFBR (project No. 10-01-00391) and by the Federal Program “Scientific and Scientific-Pedagogical Cadres of Innovative Russia” for 2009-2013 (gov. contract No. 14.740.11.0346).
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Dudkin, F.A., Sviridov, K.S. Complementing a subgroup of a hyperbolic group by a free factor. Algebra Logic 52, 222–235 (2013). https://doi.org/10.1007/s10469-013-9236-7
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DOI: https://doi.org/10.1007/s10469-013-9236-7