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)

 

The pq-condition for $3$-manifold groups


Author: Siddhartha Gadgil
Journal: Proc. Amer. Math. Soc. 129 (2001), 1873-1875
MSC (2000): Primary 57M05, 57M60
Published electronically: November 30, 2000
MathSciNet review: 1814121
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract:

We give an elementary, topological proof of the fact that any subgroup of order $pq$ of a finite $3$-manifold group is cyclic if $p$ and $q$are distinct odd primes. This condition, together with related results of Milnor and Reidemeister, implies that such a group acts orthogonally on some sphere.


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

  • 1. E. G. Mennike, Finite fundamental groups of three-dimensional manifolds, Mat. Zametki 57 (1995), no. 1, 105–117, 160 (Russian, with Russian summary); English transl., Math. Notes 57 (1995), no. 1-2, 73–81. MR 1339216 (97e:57001), http://dx.doi.org/10.1007/BF02309396
  • 2. John Milnor, Groups which act on 𝑆ⁿ without fixed points, Amer. J. Math. 79 (1957), 623–630. MR 0090056 (19,761d)
  • 3. K. Reidemeister Kommutative Fundamentalgrüppen Monatsch. Math. Phy. 43 (1935), 20-28.
  • 4. P. A. Smith, Permutable periodic transformations, Proc. Nat. Acad. Sci. U. S. A. 30 (1944), 105–108. MR 0010278 (5,274d)
  • 5. H. Zassenhaus Über endliche Fastkörper Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 79 (1936), 187-220.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 57M05, 57M60

Retrieve articles in all journals with MSC (2000): 57M05, 57M60


Additional Information

Siddhartha Gadgil
Affiliation: Department of Mathematics, SUNY at Stony Brook, Stony Brook, New York 11794
Email: gadgil@math.sunysb.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05880-9
PII: S 0002-9939(00)05880-9
Received by editor(s): October 11, 1999
Published electronically: November 30, 2000
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2000 American Mathematical Society