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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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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


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
  • MR Author ID: 191704
  • Email:
  • A. Myasnikov
  • Affiliation: Department of Mathematics, City College (CUNY), New York, New York 10031-9100
  • MR Author ID: 670299
  • Email:
  • 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:
  • MathSciNet review: 1390041