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Elementary abelian $ 2$-groups that act freely on products of real projective spaces


Author: Larry W. Cusick
Journal: Proc. Amer. Math. Soc. 87 (1983), 728-730
MSC: Primary 57S17; Secondary 57S25
DOI: https://doi.org/10.1090/S0002-9939-1983-0687651-4
MathSciNet review: 687651
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Abstract: For a natural number $ N$ let $ \bar N$ be 0 if $ N$ is even and 1 if $ N$ is odd. We prove that if $ {({Z_2})^l}$ acts freely on $ \prod_l^k{ = 1}{\mathbf{R}}{P^{{N_l}}}$ in such a way that the induced action on $ \mod 2$ cohomology is trivial, then $ l \leqslant 2({\bar N_1} + \cdots + {N_k})$. If no $ {N_l}$ is congruent to $ 3\mod 4$ then $ l \leqslant {\bar N_1} + \cdots + {\bar N_k}$.


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

  • [1] G. Carlsson, On the non-existence of free actions of elementary abelian groups on products of spheres, Amer. J. Math. 102 (1980), 1147-1157. MR 595008 (82a:57038)
  • [2] -, On the rank of abelian groups acting freely on $ {({S^n})^k}$. Invent. Math. (to appear).
  • [3] M. Greenberg, Lectures on forms in many variables, Benjamin, New York, 1969. MR 0241358 (39:2698)

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DOI: https://doi.org/10.1090/S0002-9939-1983-0687651-4
Article copyright: © Copyright 1983 American Mathematical Society

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