The cohomology rings of certain finite permutation representations

Blowers, James V.

doi:10.1090/S0002-9939-1974-0379690-2

The cohomology rings of certain finite permutation representations
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by James V. Blowers

Proc. Amer. Math. Soc. 45 (1974), 157-163

DOI: https://doi.org/10.1090/S0002-9939-1974-0379690-2

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Abstract:

In this paper the concept of join of two permutation representations is defined and the cohomology of this join is computed and shown to have trivial cup-products. This computation is then used to compute the cohomology groups of the $p$-Sylow subgroup of a symmetric group of order $n$ acting on the set of $n$ elements, and it is shown that the ring structure on these groups is not finitely generated, although it is transitive.

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