Elementary subgroups of relatively hyperbolic groups and bounded generation

International Journal of Algebra and Computation

Volumn 16, Issue 1, 2006, Pages 99-118

  Osin, Denis V ^a  

^a CITY COLLEGE OF NEW YORK   (United States)

Author keywords

Bounded generation; Elementary subgroups; Hyperbolically embedded subgroups; Relatively hyperbolic groups

Indexed keywords

EID: 33644801055     PISSN: 02181967     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218196706002901     Document Type: Article

References (26)

1. n(Z), Internat. J. Algebra Comput 2(4) (1992) 357-365.
2. B. Bekka, P. de la Harpe and A. Valette, Kazhdan's property (T) (2003), in preparation.
3. B. H. Bowditch, Geometrical finiteness with variable negative curvature, Duke Math. J. 77 (1995) 229-274.
4. B. H. Bowditch, Relatively Hyperbolic Groups (1999), in preparation.
5. M. Bridson and A. Haefliger, Metric Spaces of Non-positive Curvature (Springer, 1999).
6. n(script O sign), Amer. J. Math. 105(3) (1983) 673-687.
7. I. V. Erovenko and A. S. Rapinchuk, Bounded generation of some 5-arithmetic orthogonal groups, C. R. Acad. Sci. Paris Ser. I Math. 333(5) (2001) 395-398.
8. B. Farb, Relatively hyperbolic groups, GAFA 8, (1998) 810-840.
9. S. Gersten, Subgroups of small cancellation groups in dimension 2, J. London Math. Sac. 54 (1996) 261-283.
10. E. Ghys and P. de la Harpe, eds., Sur les groupes hyperboliques d'aprés Mikhael Gromov, Progress in Math., Vol. 83 (Birkhaüser, 1990).
11. M. Gromov, Hyperbolic Groups, Essays in Group Theory, MSRI Series, Vol. 8, ed. S. M. Gersten (Springer, 1987), pp. 75-263.
12. S. V. Ivanov and A. Yu. Olshanskii, Hyperbolic groups and their quotients of bounded exponents, Trans. Amer. Math. Soc. 348(6) (1996) 2091-2138.
13. M. V. Kumar, Bounded and finite generation of arithmetic groups, in Number Theory, Halifax, NS, 1994, CMS Conference Proceedings, Vol. 15 (Amer. Math. Soc., Providence, RI, 1995), pp. 249-261.
14. A. Lubotzky and D. Segal, Subgroup growth. Progress in Mathematics, Vol. 212 (Birkhaüser Verlag, Basel, 2003).
15. R. C. Lyndon and P. E. Shupp, Combinatorial Group Theory (Springer-Verlag, 1977).
16. A. Minasyan, On products of qusi-convex subgroups in hyperbolic groups, Int. J. Alg. Cornp., to appear.
17. A. Yu. Olshanskii, Periodic quotients of hyperbolic groups, Mat. Sbornik 182(4) (1991) 543-567 (in Russian),
18. English translation in Math. USSR, Sbornik 72(2) (1992) 519-541.
19. A. Yu. Olshanskii, On residualing homomorphisms and G-subgroups of hyperbolic groups, Int. J. Alg. Comp. 3(4) (1993) 365-409.
20. D. V. Osin, Relatively hyperbolic groups: intrinsic geometry, algebraic properties, and algorithmic problems, Memoirs Amer. Math. Soc. 179 (2006), no. 843.
21. D. V. Osin, Relatively hyperbolic groups and embedding theorems, available at http://www.arxiv.org/abs/math.GR./0411039.
22. A. S. Rapinchuk, The congruence subgroup problem for arithmetic groups of bounded generation (in Russian), Dokl. Akad. Nauk SSSR 314(6) (1990) 1327-1331;
23. translation in Soviet Math. Dokl. 42(2) (1991) 664-668.
24. Y. Shalom, Bounded generation and Kazhdan's property (T), IHES Sci. Publ. Math. 90 (1999) 145-168.
25. I. O. Tavgen', Bounded generability of Chevalley groups over rings of S-integer algebraic numbers (in Russian) Izv. Akad. Nauk SSSR Ser. Mat. 54(1) (1990) 97-122, 221-222;
26. translation in Math. USSR-lzv. 36(1) (1991) 101-128.