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Hyperbolic groups and free constructions


Authors: O. Kharlampovich and A. Myasnikov
Journal: Trans. Amer. Math. Soc. 350 (1998), 571-613
MSC (1991): Primary 20F06, 20E06
DOI: https://doi.org/10.1090/S0002-9947-98-01773-5
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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Additional Information

O. Kharlampovich
Affiliation: Department of Mathematics and Statistics, McGill University, Montréal, P.Q., Canada H3A 2K6
Email: olga@triples.math.mcgill.ca

A. Myasnikov
Affiliation: Department of Mathematics, City College (CUNY), New York, New York 10031-9100
Email: alexei@rio.sci.ccny.cuny.edu

DOI: https://doi.org/10.1090/S0002-9947-98-01773-5
Received by editor(s): July 7, 1994
Received by editor(s) in revised form: January 18, 1996
Additional Notes: The first author was supported by grants from NSERC and FCAR
Article copyright: © Copyright 1998 American Mathematical Society

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