Smith theory for𝑝-groups

Maiorana, James A.

doi:10.1090/S0002-9947-1976-0423387-3

Smith theory for$p$-groups
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by James A. Maiorana

Trans. Amer. Math. Soc. 223 (1976), 253-266

DOI: https://doi.org/10.1090/S0002-9947-1976-0423387-3

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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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A cohomology invariant for finite groups

Cohomology of p-groups

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