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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The cohomology rings of certain finite permutation representations

Author: James V. Blowers
Journal: Proc. Amer. Math. Soc. 45 (1974), 157-163
MSC: Primary 20J05
MathSciNet review: 0379690
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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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Keywords: Join of permutation representations, projective resolution, suspended chain complex, wreath product, spectral sequence, cup-products, $ p$-Sylow subgroup, symmetric group, transitive permutation representation, finite generation, cohomology of permutation representations
Article copyright: © Copyright 1974 American Mathematical Society