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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Smith theory for$ p$-groups


Author: James A. Maiorana
Journal: Trans. Amer. Math. Soc. 223 (1976), 253-266
MSC: Primary 57E10
MathSciNet review: 0423387
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Abstract: When a p-group G acts on a manifold, the behavior of the cohomology of the subgroups of G singles out a special collection of fixed point sets of these subgroups. A bound on the size of the spaces in this collection is derived using equivariant cohomology. For a special class of nonabelian p-groups this bound is strong enough to require that certain fixed point sets must vanish. Application of this bound to a linear representation of G yields a lower bound for the cohomology of G.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1976-0423387-3
PII: S 0002-9947(1976)0423387-3
Keywords: Smith theory, p-group, cohomology of groups, fixed point sets of subgroups
Article copyright: © Copyright 1976 American Mathematical Society