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Transactions of the American Mathematical Society

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

 
 

 

Equations in the Q-completion of
a torsion-free hyperbolic group


Authors: O. Kharlampovich, E. Lioutikova and A. Myasnikov
Journal: Trans. Amer. Math. Soc. 351 (1999), 2961-2978
MSC (1991): Primary 20E05, 20F10
DOI: https://doi.org/10.1090/S0002-9947-99-02010-3
Published electronically: March 1, 1999
MathSciNet review: 1443195
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we prove the algorithmic solvability of finite systems of equations over the Q-completion of a torsion-free hyperbolic group.


References [Enhancements On Off] (What's this?)

  • 1. O. Kharlampovich, A. Myasnikov. Equations in a free Q-group. Trans. Amer. Math. Soc. 350 (1998), 947-974. CMP 98:05
  • 2. O. Kharlampovich, A. Myasnikov. Hyperbolic groups and free constructions. Trans. Amer. Math. Soc. 350 (1998), 571-613.
  • 3. A. Yu. Ol'shanskii. On residualing homomorphisms and G-subgroups of hyperbolic groups. International Journal of Algebra and Computation, 3(4):365-409, 1993. MR 94i:20069
  • 4. E. Rips and Z. Sela. Canonical representatives and equations in hyperbolic groups. Invent. Math., 120: 489-512, 1995. MR 96c:20053
  • 5. Thomas Delzant. Finitely presented subgroups of hyperbolic groups. (Preprint)
  • 6. G. S. Makanin. Equations in a free group. Math. USSR Izv., V. 21, 1983. MR 84m:20040

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Additional Information

O. Kharlampovich
Affiliation: Department of Mathematics and Statistics, McGill University, 805 Sherbrooke St. West, Montreal, Quebec, H3A 2K6 Canada
Email: olga@triples.math.mcgill.ca

E. Lioutikova
Affiliation: Department of Mathematics and Statistics, McGill University, 805 Sherbrooke St. West, Montreal, Quebec, H3A 2K6, Canada
Email: kate@triples.math.mcgill.ca

A. Myasnikov
Affiliation: Department of Mathematics, City College (CUNY), Convent Ave. at 138th Street, New York, New York 10031-9100
Email: alexei@jolly2.sci.ccny.cuny.edu

DOI: https://doi.org/10.1090/S0002-9947-99-02010-3
Received by editor(s): August 14, 1996
Published electronically: March 1, 1999
Additional Notes: The first author was supported by grants from NSERC and FCAR
The third author was supported by the NSF grant DMS-9103098
Article copyright: © Copyright 1999 American Mathematical Society

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