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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
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Abstract | References | Similar Articles | Additional Information


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?)

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  • 2. John Milnor, Groups which act on 𝑆ⁿ without fixed points, Amer. J. Math. 79 (1957), 623–630. MR 0090056 (19,761d)
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Additional Information

Siddhartha Gadgil
Affiliation: Department of Mathematics, SUNY at Stony Brook, Stony Brook, New York 11794

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

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