Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Simple quotients of hyperbolic 3-manifold groups


Authors: D. D. Long and A. W. Reid
Journal: Proc. Amer. Math. Soc. 126 (1998), 877-880
MSC (1991): Primary 57M50, 57M60, 57R30
MathSciNet review: 1459136
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We show that hyperbolic $3$-manifolds have residually simple fundamental group.


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

  • 1. Hyman Bass, Groups of integral representation type, Pacific J. Math. 86 (1980), no. 1, 15–51. MR 586867 (82c:20014)
  • 2. Władysław Narkiewicz, Elementary and analytic theory of algebraic numbers, PWN—Polish Scientific Publishers, Warsaw, 1974. Monografie Matematyczne, Tom 57. MR 0347767 (50 #268)
  • 3. Michio Suzuki, Group theory. I, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 247, Springer-Verlag, Berlin, 1982. Translated from the Japanese by the author. MR 648772 (82k:20001c)
  • 4. W. P. Thurston, The Geometry and Topology of 3-Manifolds, Mimeographed lecture notes, Princeton University, 1977.
  • 5. Marie-France Vignéras, Arithmétique des algèbres de quaternions, Lecture Notes in Mathematics, vol. 800, Springer, Berlin, 1980 (French). MR 580949 (82i:12016)
  • 6. B. A. F. Wehrfritz, Infinite linear groups. An account of the group-theoretic properties of infinite groups of matrices, Springer-Verlag, New York, 1973. Ergebnisse der Matematik und ihrer Grenzgebiete, Band 76. MR 0335656 (49 #436)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 57M50, 57M60, 57R30

Retrieve articles in all journals with MSC (1991): 57M50, 57M60, 57R30


Additional Information

D. D. Long
Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106
Email: long@math.ucsb.edu

A. W. Reid
Affiliation: Department of Mathematics, University of Texas, Austin, Texas 78712
Email: areid@math.utexas.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04458-X
PII: S 0002-9939(98)04458-X
Keywords: $3$-manifold, residually simple.
Received by editor(s): November 28, 1995
Additional Notes: Supported by the NSF (both authors) and The Royal Society (second author)
Communicated by: James West
Article copyright: © Copyright 1998 American Mathematical Society