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Free Actions of Abelian Groups on a Cartesian Power of an Even Sphere

Published online by Cambridge University Press:  20 November 2018

Michael Hoffman
Michael Hoffman*
Affiliation:
Department of Mathematics U.S. Naval Academy
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Abstract

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We determine an algebraic condition necessary and sufficient for a group G to act freely on the nth Cartesian power of an even sphere, and characterize the abelian groups that satisfy this condition.

Keywords

Primary 57S25Secondary 57S17
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 3 , 01 September 1987 , pp. 358 - 362
Copyright
Copyright © Canadian Mathematical Society 1987

References

1. Gunnar, Carlsson, On the rank of abelian groups acting freely on (Sn)k , Invent, math. 69 (1982), pp. 393–400.Google Scholar
2. Nobuaki, Yogita, On the dimension of spheres whose product admits a free action by a nonabelian group, Quart. J. Math. 36 (1985), pp. 117–127.Google Scholar