Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Equations in the Q-completion of a torsion-free hyperbolic group
HTML articles powered by AMS MathViewer

by O. Kharlampovich, E. Lioutikova and A. Myasnikov PDF
Trans. Amer. Math. Soc. 351 (1999), 2961-2978 Request permission

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
  • O. Kharlampovich, A. Myasnikov. Equations in a free Q–group. Trans. Amer. Math. Soc. 350 (1998), 947–974.
  • O. Kharlampovich, A. Myasnikov. Hyperbolic groups and free constructions. Trans. Amer. Math. Soc. 350 (1998), 571–613.
  • A. Yu. Ol′shanskiĭ, On residualing homomorphisms and $G$-subgroups of hyperbolic groups, Internat. J. Algebra Comput. 3 (1993), no. 4, 365–409. MR 1250244, DOI 10.1142/S0218196793000251
  • E. Rips and Z. Sela, Canonical representatives and equations in hyperbolic groups, Invent. Math. 120 (1995), no. 3, 489–512. MR 1334482, DOI 10.1007/BF01241140
  • Thomas Delzant. Finitely presented subgroups of hyperbolic groups. (Preprint)
  • G. S. Makanin, Equations in a free group, Izv. Akad. Nauk SSSR Ser. Mat. 46 (1982), no. 6, 1199–1273, 1344 (Russian). MR 682490
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 20E05, 20F10
  • Retrieve articles in all journals with MSC (1991): 20E05, 20F10
Additional Information
  • O. Kharlampovich
  • Affiliation: Department of Mathematics and Statistics, McGill University, 805 Sherbrooke St. West, Montreal, Quebec, H3A 2K6 Canada
  • MR Author ID: 191704
  • 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
  • MR Author ID: 670299
  • Email: alexei@jolly2.sci.ccny.cuny.edu
  • 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
  • © Copyright 1999 American Mathematical Society
  • 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
  • MathSciNet review: 1443195