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

Author(s): O. Kharlampovich; E. Lioutikova; A. Myasnikov
Journal: Trans. Amer. Math. Soc. 351 (1999), 2961-2978.
MSC (1991): Primary 20E05, 20F10
Posted: March 1, 1999
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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:

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: 10.1090/S0002-9947-99-02010-3
PII: S 0002-9947(99)02010-3
Received by editor(s): August 14, 1996
Posted: 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
Copyright of article: Copyright 1999, American Mathematical Society

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