Implicit function theorem over free groups

Journal of Algebra

Volumn 290, Issue 1, 2005, Pages 1-203

  Kharlampovich, Olga ^a   Myasnikov, Alexei ^b  

^a MCGILL UNIVERSITY   (Canada)

^b CITY COLLEGE OF NEW YORK   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21844453641     PISSN: 00218693     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jalgebra.2005.04.001     Document Type: Article

References (28)

1. S.I. Adian Burnside Problem and Identities in Groups 1975 Science Moscow
2. H. Bass Groups acting on non-archimedian trees in: Arboreal Group Theory 1991 69-130
3. G. Baumslag A. Myasnikov V. Remeslennikov Algebraic geometry over groups I. Algebraic sets and ideal theory J. Algebra 219 1999 16-79
4. G. Baumslag A. Myasnikov V. Remeslennikov Residually hyperbolic groups Proc. Inst. Appl. Math. Russian Acad. Sci. 24 1995 3-37
5. R. Bryant The verbal topology of a group J. Algebra 48 1977 340-346
6. C.C. Chang H.J. Keisler Model Theory 1973 North-Holland London
7. L.P. Comerford C.C. Edmunds Quadratic equations over free groups and free product J. Algebra 68 1981 276-297
8. D. Gildenhuys O. Kharlampovich A. Myasnikov CSA groups and separated free constructions Bull. Aust. Math. Soc. 52 1995 63-84
9. R.I. Grigorchuk P.F. Kurchanov On quadratic equations in free groups Contemp. Math. 131 1 1992 159-171
10. V. Guba Equivalence of infinite systems of equations in free groups and semigroups to finite subsystems Mat. Zametki 40 1986 321-324
11. O. Kharlampovich A. Myasnikov Description of fully residually free groups and irreducible affine varieties over a free group in: CRM Proc. Lecture Notes vol. 17 1999 Center de Recherchers Matematiques 71-80
12. O. Kharlampovich A. Myasnikov Irreducible affine varieties over a free group I: Irreducibility of quadratic equations and Nullstellensatz J. Algebra 200 1998 472-516
13. O. Kharlampovich A. Myasnikov Irreducible affine varieties over a free group II: Systems in triangular quasi-quadratic form and description of residually free groups J. Algebra 200 2 1998 517-570
14. O. Kharlampovich A. Myasnikov Tarski' problem about the elementary theory of free nonabelian groups has a positive solution Electron. Res. Announc. Amer. Math. Soc. 4 1998 101-108
15. O. Kharlampovich A. Myasnikov Implicit function theorem over free groups and genus problem in: AMS/IP Stud. Adv. Math. vol. 24 2001 77-83
16. O. Kharlampovich A. Myasnikov Elementary theory of free non-abelian groups McGill University Preprint http://www.math.mcgill.ca/olga/publications.html 1999
17. 2 in free groups Michigan Math. J. 6 1959 155-164
18. R.C. Lyndon P.E. Schupp Combinatorial Group Theory 1977 Springer
19. G.S. Makanin Equations in a free group Izv. Akad. Nauk SSSR Ser. Mat. 46 1982 1199-1273 (in Russian). Translation in Math. USSR Izv. 21 (1983). MR 84m:20040
20. G.S. Makanin Decidability of the universal and positive theories of a free group Izv. Akad. Nauk SSSR Ser. Mat. 48 1 1985 735-749 (in Russian). Translation in Math. USSR Izv. 25 (1985). MR 86c:03009.
21. -1 in a free group Algebra i Logika Sem. 1 5 1962 45-50 (in Russian)
22. Ju.I. Merzljakov Positive formulae on free groups Algebra i Logika 5 4 1966 25-42
23. http://msri.org/publications/ln/msri/1998/mtf
24. A. Myasnikov, A. Kvaschuk, Big powers and free constructions, Internat. J. Algebra Comput., in press
25. A.G. Myasnikov V.N. Remeslennikov Exponential groups 2: Extension of centralizers and tensor completion of csa-groups Internat. J. Algebra Comput. 6 6 1996 687-711
26. A.Yu. Ol'shanskii On residualing homomorphisms and G-subgroups of hyperbolic groups Internat. J. Algebra Comput. 3 4 1993 365-409
27. A. Razborov, On systems of equations in a free group, PhD thesis, Steklov Math. Institute, Moscow, 1987
28. V.N. Remeslennikov E-free groups Siberian Math. J. 30 6 1989 153-157