The SQ-universality and residual properties of relatively hyperbolic groups

Journal of Algebra

Volumn 315, Issue 1, 2007, Pages 165-177

  Arzhantseva, G ^a   Minasyan, A ^a   Osin, D ^b  

^a UNIVERSITY OF GENEVA   (Switzerland)

^b CITY COLLEGE OF NEW YORK   (United States)

Author keywords

Relatively hyperbolic groups; SQ universality

Indexed keywords

EID: 34547419194     PISSN: 00218693     EISSN: 1090266X     Source Type: Journal    
DOI: 10.1016/j.jalgebra.2007.04.029     Document Type: Article

References (26)

1. Bass H., and Lubotzky A. Nonarithmetic superrigid groups: Counterexamples to Platonov's conjecture. Ann. of Math. 151 3 (2000) 1151-1173
2. Baumslag B., and Pride S.J. Groups with two more generators than relators. J. London Math. Soc. (2) 17 3 (1978) 425-426
3. B.H. Bowditch, Relatively hyperbolic groups, preprint, Southampton, 1998
4. Dahmani F. Combination of convergence groups. Geom. Topol. 7 (2003) 933-963
5. Drutu C., and Sapir M. Tree graded spaces and asymptotic cones, with appendix by D. Osin and M. Sapir. Topology 44 5 (2005) 959-1058
6. Farb B. Relatively hyperbolic groups. Geom. Funct. Anal. 8 5 (1998) 810-840
7. Fine B., and Tretkoff M. On the SQ-universality of HNN groups. Proc. Amer. Math. Soc. 73 3 (1979) 283-290
8. Fine B. On power conjugacy and SQ-universality for Fuchsian and Kleinian groups. Modular Functions in Analysis and Number Theory. Lecture Notes Math. Statist. vol. 5 (1983), Univ. Pittsburgh, Pittsburgh, PA 41-54
9. Gromov M. Hyperbolic groups. In: Gersten S.M. (Ed). Essays in Group Theory. Math. Sci. Res. Inst. Publ. vol. 8 (1987), Springer-Verlag 75-263
10. n-trees. Geom. Topol. 8 (2004) 1427-1470
11. Higman G., Neumann B.H., and Neumann H. Embedding theorems for groups. J. London Math. Soc. 24 (1949) 247-254
12. Howie J. On the SQ-universality of T (6)-groups. Forum Math. 1 3 (1989) 251-272
13. Hruska G.C., and Kleiner B. Hadamard spaces with isolated flats. Geom. Topol. 9 (2005) 1501-1538
14. Lossov K.I. SQ-universality of free products with amalgamated finite subgroups. Sibirsk. Mat. Zh. 27 6 (1986) 128-139 225 (in Russian)
15. Miller III Ch.F. Decision problems for groups-Survey and reflections. Algorithms and Classification in Combinatorial Group Theory. Berkeley, CA, 1989. Math. Sci. Res. Inst. Publ. vol. 23 (1992), Springer-Verlag, New York 1-59
16. Neumann B.H. Groups covered by permutable subsets. J. London Math. Soc. 29 (1954) 236-248
17. Olshanskii A.Yu. On the Bass-Lubotzky question about quotients of hyperbolic groups. J. Algebra 226 2 (2000) 807-817
18. Olshanskii A.Yu. SQ-universality of hyperbolic groups. Mat. Sb. 186 8 (1995) 119-132 (in Russian)
19. Olshanskii A.Yu. SQ-universality of hyperbolic groups. Sb. Math. 186 8 (1995) 1199-1211
20. Osin D.V. Elementary subgroups of relatively hyperbolic groups and bounded generation. Internat. J. Algebra Comput. 16 1 (2006) 99-118
21. Osin D.V. Relatively hyperbolic groups: Intrinsic geometry, algebraic properties, and algorithmic problems. Mem. Amer. Math. Soc. 179 843 (2006) vi+100 pp
22. D.V. Osin, Small cancellations over relatively hyperbolic groups and embedding theorems, Ann. of Math., in press
23. Ratcliffe J. Euler characteristics of 3-manifold groups and discrete subgroups of SL (2, C). Proceedings of the Northwestern Conference on Cohomology of Groups. Evanston, IL, 1985. J. Pure Appl. Algebra 44 1-3 (1987) 303-314
24. Sacerdote G.S., and Schupp P.E. SQ-universality in HNN groups and one relator groups. J. London Math. Soc. (2) 7 (1974) 733-740
25. Schupp P.E. A survey of SQ-universality. Conference on Group Theory. Univ. Wisconsin-Parkside, Kenosha, WI, 1972. Lecture Notes in Math. vol. 319 (1973), Springer-Verlag, Berlin 183-188
26. Stallings J. Group Theory and Three-Dimensional Manifolds. Yale Mathematical Monographs vol. 4 (1971), Yale University Press, New Haven, CT