Transactions of the American Mathematical Society

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ISSN 1088-6850(e) ISSN 0002-9947(p)

Hyperbolic groups and free constructions

Author(s): O. Kharlampovich; A. Myasnikov
Journal: Trans. Amer. Math. Soc. 350 (1998), 571-613.
MSC (1991): Primary 20F06, 20E06
MathSciNet review: 1390041
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Abstract: It is proved that the property of a group to be hyperbolic is preserved under HHN-extensions and amalgamated free products provided the associated (amalgamated) subgroups satisfy certain conditions. Some more general results about the preservation of hyperbolicity under graph products are also obtained. Using these results we describe the $\mathbf{Q}$ -completion $(\mathbf{Q}$ is the field of rationals) $G^{\mathbf{Q}}$ of a torsion-free hyperbolic group $G$ as a union of an effective chain of hyperbolic subgroups, and solve the conjugacy problem in $G^{\mathbf{Q}}$ .

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