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Equations in a free  -group
Author(s):
O.
Kharlampovich;
A.
Myasnikov
Journal:
Trans. Amer. Math. Soc.
350
(1998),
947-974.
MSC (1991):
Primary 20E05, 20F10
MathSciNet review:
1389782
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Abstract |
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Abstract:
An algorithm is constructed that decides if a given finite system of equations over a free  -group has a solution, and if it does, finds a solution.
References:
- 1.
- G Baumslag, On free
 -group, Comm. Pure and Appl. Math., 18 (1965) 25-30. MR 31:1293 - 2.
- -, Some aspects of groups with unique roots, Acta Math., 104 (1960), 217-303. MR 23:A191
- 3.
- G. Baumslag, A. Myasnikov, and V. Remeslennikov, Residually hyperbolic groups, preprint, 1996.
- 4.
- L. P. Comerford Jr., and C. C. Edmunds, Solutions of equations in free groups, Group Theory (Singapore, 1987; K. N. Cheng and Y. K. Leong, editors), de Gruyter, Berlin, 1989, pp. 347-356. MR 90a: 20067
- 5.
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- 6.
- O. Kharlampovich and A. G. Myasnikov, Hyperbolic groups and free constructions, Trans. Amer. Math. Soc. 350 (1998), 571-613.
- 7.
- G.S. Makanin, Decidability of the universal and positive theories of a free group, Izv. Akad. Nauk SSSR, Ser. Mat. 48 (1984), 735-749; English transl., Math. USSR Izv. 25, (1985), 75-88. MR 86c:03009.
- 8.
- -, Equations in a free group, Izv. Akad. Nauk SSSR, Ser. Mat. 46 (1982), 1199-1273; English transl., Math. USSR Izv. 21 (1983), 483-546. MR 84m:20040
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- H. Presburger, Über die Vollständigkeit eines gewissen Systems der Arithmetik ganzen Zahlen, C. R. 1 Congr. Math. Pays Slaves, Warsaw, 1929, pp. 92-101.
- 11.
- A. A. Razborov, On systems of equations in a free group, Izv. Akad. Nauk SSSR Ser. Mat. 48 (1984), 779-832; English transl., Math. USSR Izv. 25 (1985), 115-162. MR 86c:20033
- 12.
- E. Rips and Z. Sela, Canonical representatives and equations in hyperbolic groups, Invent. Math. 120 (1995), 489-512. MR 96c:20053
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Additional Information:
O.
Kharlampovich
Affiliation:
Department of Mathematics and Statistics, McGill University, Montréal, P.Q., Canada H3A 2K6
Email:
olga@triples.math.mcgill.ca
A.
Myasnikov
Affiliation:
Department of Mathematics, City College (CUNY), Convent Avenue and 138th Street, New York, New York 10031-9100
Email:
alexei@rio.sci.ccny.cuny.edu
DOI:
10.1090/S0002-9947-98-01798-X
PII:
S 0002-9947(98)01798-X
Received by editor(s):
April 5, 1996
Additional Notes:
The first author was supported by grants from NSERC and FCAR; the second author was supported by the NSF Grant DMS-9103098
Copyright of article:
Copyright
1998,
American Mathematical Society
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