Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the SQ-universality of HNN groups

Authors: Benjamin Fine and Marvin Tretkoff
Journal: Proc. Amer. Math. Soc. 73 (1979), 283-290
MSC: Primary 20E34
MathSciNet review: 518506
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A group G is SQ-universal if every countable group can be embedded in a quotient of G. In this paper we give conditions under which HNN groups are SQ-universal. These are then applied to showing the SQ-universality of certain classes of Kleinian groups (discontinuous subgroups of $ PS{L_2}({\mathbf{C}})$. Finally some connections are mentioned between SQ-universality and the theory of ends.

References [Enhancements On Off] (What's this?)

  • [1] D. E. Cohen, Groups of cohomological dimension one, Lecture Notes in Math., vol. 245, Springer-Verlag, Berlin and New York, 1972. MR 0344359 (49:9098)
  • [2] B. Fine, The HNN and generalized free product structure of certain linear groups, Bull. Amer. Math. Soc. 81 (1976), 413-416. MR 0372059 (51:8276)
  • [3] B. Fine and M. Tretkoff, The SQ-universality of certain arithmetically defined linear groups, J. London Math. Soc. (2) 13 (1976), 65-68. MR 0407164 (53:10947)
  • [4] G. Higman, B. H. Neumann and H. Neumann, Embedding theorems for groups, J. London Math. Soc. 24 (1949), 247-254. MR 0032641 (11:322d)
  • [5] A. Karrass and D. Solitar, Subgroups of HNN groups and groups with one defining relation, Canad. J. Math. 23 (1971), 627-643. MR 0301102 (46:260)
  • [6] J. Lehner, Discontinuous groups and automorphic functions, Math. Surveys, No. 8, Amer. Math. Soc., Providence, R. I., 1964. MR 0164033 (29:1332)
  • [7] B. Maskit, On Klein's combination theorem. III, Advances in the Theory of Riemann Surfaces, Ann. of Math. Studies, No. 66, Princeton Univ. Press, Princeton, N. J., 1971, pp. 297-316. MR 0289768 (44:6955)
  • [8] P. M. Neumann, The SQ-universality of some finitely presented groups, J. Austral. Math. Soc. 16 (1973), 1-6. MR 0333017 (48:11342)
  • [9] G. Sacerdote and P. Schupp, SQ-universality in HNN groups and one-relator groups, J. London Math. Soc. (2) 7 (1974), 733-740. MR 0364464 (51:718)
  • [10] P. Schupp, Small cancellation theory over free products with amalgamation, Math. Ann. 193 (1971), 255-264. MR 0291298 (45:392)
  • [11] M. Tretkoff, Covering space proofs in combinatorial group theory, Comm. Algebra 3 (1975), 429-457. MR 0417298 (54:5355)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20E34

Retrieve articles in all journals with MSC: 20E34

Additional Information

Keywords: SQ-universal, HNN group, generalized free product, Kleinian group, Fuchsian group, Klein's combination theorem, ends of a group
Article copyright: © Copyright 1979 American Mathematical Society

American Mathematical Society