Subgroup conditions for groups acting freely on products of spheres

Author:
Judith H. Silverman

Journal:
Trans. Amer. Math. Soc. **334** (1992), 153-181

MSC:
Primary 55M35; Secondary 55N91

DOI:
https://doi.org/10.1090/S0002-9947-1992-1100700-4

MathSciNet review:
1100700

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Abstract | References | Similar Articles | Additional Information

Abstract: Let and be integers such that either and , or and . Suppose that the group contains an elementary-abelian -subgroup of rank with an element of order in its normalizer. We show that if admits a free and -cohomologically trivial action on , then some nontrivial power of centralizes .

The cohomology ring is a module over the Steenrod algebra . Let , and let be an integer. We show that divides in the polynomial ring for , where divides for and is a product of linear forms.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1992-1100700-4

Keywords:
Steenrod algebra,
free group actions

Article copyright:
© Copyright 1992
American Mathematical Society