The isomorphism problem for finitely generated fully residually free groups

Journal of Pure and Applied Algebra

Volumn 208, Issue 3, 2007, Pages 961-977

  Bumagin, Inna ^a   Kharlampovich, Olga ^b   Miasnikov, Alexei ^b  

^a CARLETON UNIVERSITY   (Canada)

^b MCGILL UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33751348302     PISSN: 00224049     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jpaa.2006.03.025     Document Type: Article

References (35)

1. Bass H. Group actions on non-Archimedean trees. Arboreal Group Theory (Berkeley, CA, 1988). Math. Sci. Res. Inst. Publ. vol. 19 (1991), Springer, New York 69-131
2. Baumslag B. Residually free groups. Proc. London Math. Soc. 17 3 (1967) 402-418
3. Baumslag G., Miasnikov A., and Remeslennikov V. Algebraic geometry over groups I. Algebraic sets and ideal theory. J. Algebra 219 (1999) 16-79
4. Bowditch B. Cut points and canonical splittings of hyperbolic groups. Acta Math. 180 2 (1998) 145-186
5. Bumagin I. The conjugacy problem for relatively hyperbolic groups. Algebr. Geom. Topol. 4 (2004) 1013-1040
6. I. Bumagin, D. Wise, Coherence of coherent-by-cyclic groups, preprint
7. Dahmani F. Combination of convergence groups. Geom. Topol. 7 (2003) 933-963
8. Farb B. Relatively hyperbolic groups. GAFA 8 (1998) 810-840
9. Forester M. Deformation and rigidity of simplicial group actions on trees. Geom. Topol. 6 (2002) 219-267
10. Forester M. On uniqueness of JSJ decompositions of finitely generated groups. Comment. Math. Helv. 78 (2003) 740-751
11. Gildenhuys D., Kharlampovich O., and Myasnikov A. CSA-groups and separated free constructions. Bull. Austral. Math. Soc. 52 (1995) 63-84
12. Guirardel V. A very short proof of Forester's rigidity result. Geom. Topol. 7 (2003) 321-328
13. Kharlampovich O., and Myasnikov A. Irreducible affine varieties over a free group II. J. Algebra 200 (1998) 517-570
14. Kharlampovich O., and Myasnikov A. Implicit function theorem over free groups. J. Algebra 290 (2005) 1-203
15. Kharlampovich O., and Myasnikov A. Effective JSJ decompositions. In: Borovik A. (Ed). Group Theory: Algorithms, Languages, Logic. Contemp. Math. vol. 378 (2005), Amer. Math. Soc. 87-212
16. Kharlampovich O., Myasnikov A., Remeslennikov V., and Serbin D. Subgroups of fully residually free groups: algorithmic problems. In: Myasnikov A.G., and Shpilrain V. (Eds). Group Theory, Statistics and Cryptography. Contemp. Math. vol. 360 (2004), Amer. Math. Soc.
17. Kurosh A.G. In: Hirsch. K.A. (Ed). The Theory of Groups. 2nd English ed. (1960), Chelsea Publishing Co, New York (Translated from the Russian)
18. Levitt G. Automorphisms of hyperbolic groups and graphs of groups. Geom. Dedicata 114 (2005) 49-70
19. Lyndon R.C. Groups with parametric exponents. Trans. Amer. Math. Soc. 96 (1960) 518-533
20. Lyndon R.C. Equations in free groups. Trans. Amer. Math. Soc. 96 (1960) 445-457
21. Lyndon R.C., and Schupp P. Combinatorial Group Theory. Ergebnisse der Mathematik und ihrer Grenzgebiete Band 89 (1977), Springer-Verlag, Berlin, New York
22. Makanin G.S. Equations in a free group. Math. USSR Izv. 21 (1983)
23. Makanin G.S. Decidability of the universal and positive theories of a free group. Izv. Akad. Nauk SSSR, Ser. Mat. 48 1 (1985) 735-749 (in Russian). Transl. in Math. USSR Izv., 25 (1985) MR 86c:03009
24. Z [t]. In: Borovik A. (Ed). Group Theory: Algorithms, Languages, Logic. Contemp. Math. vol. 378 (2005), Amer. Math. Soc. 37-77
25. Osin D. Relatively hyperbolic groups: intrinsic geometry, algebraic properties, and algorithmic problems. Mem. Amer. Math. Soc. 179 843 (2006)
26. Razborov A. On systems of equations in a free group. Math. USSR-Izv. 25 1 (1985) 115-162
27. Rips E., and Sela Z. Canonical representatives and equations in hyperbolic groups. Invent. Math. 120 3 (1995) 489-512
28. Rips E., and Sela Z. Cyclic splittings of finitely presented groups and the canonical JSJ decomposition. Ann. Math. 146 (1997) 53-104
29. Segal D. Decidable properties of polycyclic groups. Proc. London Math. Soc. (3) 61 3 (1990) 497-528
30. Segal D., and Grunewald F.J. Some general algorithms. II. Nilpotent groups. Ann. of Math. (2) 112 3 (1980) 531-617
31. Sela Z. The isomorphism problem for hyperbolic groups. I. Ann. of Math. 141 2 (1995) 217-283
32. Sela Z. Structure and rigidity in (Gromov) hyperbolic groups and discrete groups in rank 1 Lie groups II. GAFA 7 (1997) 561-593
33. Sela Z. Diophantine geometry I. Publ. Math. IHES 93 (2001) 31-105
34. Serre J.P. Trees (1980), Springer-Verlag, Berlin, New York
35. F. Dahmani, D. Groves, The isomorphism problem for toral relatively hyperbolic groups, preprint