Some restrictions on finite groups acting freely on

Author:
Gunnar Carlsson

Journal:
Trans. Amer. Math. Soc. **264** (1981), 449-457

MSC:
Primary 55M35; Secondary 55S10

MathSciNet review:
603774

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Abstract: Restrictions other than rank conditions on elementary abelian subgroups are found for finite groups acting freely on , with trivial action on homology. It is shown that elements of order , an odd prime, with in the normalizer of an elementary abelian -subgroup of , must act trivially on unless . It is also shown that if or , must act trivially, independent of . This produces a large family of groups which do not act freely on for any values of and . For certain primes , using the mod two Steenrod algebra, one may show that acts trivially unless , where is an integer depending on .

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DOI:
https://doi.org/10.1090/S0002-9947-1981-0603774-2

Article copyright:
© Copyright 1981
American Mathematical Society