## Hyperbolic groups and free constructions

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- by O. Kharlampovich and A. Myasnikov PDF
- Trans. Amer. Math. Soc.
**350**(1998), 571-613 Request permission

## 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 $G^{\mathbf {Q}}$.## References

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## Additional Information

**O. Kharlampovich**- Affiliation: Department of Mathematics and Statistics, McGill University, Montréal, P.Q., Canada H3A 2K6
- MR Author ID: 191704
- Email: olga@triples.math.mcgill.ca
**A. Myasnikov**- Affiliation: Department of Mathematics, City College (CUNY), New York, New York 10031-9100
- MR Author ID: 670299
- Email: alexei@rio.sci.ccny.cuny.edu
- 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
- © Copyright 1998 American Mathematical Society
- 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