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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$.

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

  • [1] L. W. Cusick, Finite groups that can act freely on products of even dimensional spheres, Indiana Univ. Math. J. 35 (1986), 175-178. MR 825634 (87e:57038)
  • [2] L. W. Cusick and P. Tannenbaum, Fixed points of the binary shift (to appear).

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Article copyright: © Copyright 1987 American Mathematical Society

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