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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Free actions on products of even-dimensional spheres


Author: Larry W. Cusick
Journal: Proc. Amer. Math. Soc. 99 (1987), 573-574
MSC: Primary 57S25; Secondary 57S17
MathSciNet review: 875401
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Abstract: We show that if $ G$ is a finite group acting freely on $ \prod _{j = 1}^k{S^{2{n_j}}}$ and if the induced action on $ (\bmod 2)$ homology is trivial, then 2 for some $ l \leq k$. We also show that if $ G$ acts freely on $ G$ and $ G$ is cyclic of order $ {2^l}$, then $ {2^{l - 1}} \leq k$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0875401-1
PII: S 0002-9939(1987)0875401-1
Article copyright: © Copyright 1987 American Mathematical Society