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 | References | Similar Articles | Additional Information

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 -Sylow subgroup of a symmetric group of order acting on the set of elements, and it is shown that the ring structure on these groups is not finitely generated, although it is transitive.

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

Keywords:
Join of permutation representations,
projective resolution,
suspended chain complex,
wreath product,
spectral sequence,
cup-products,
-Sylow subgroup,
symmetric group,
transitive permutation representation,
finite generation,
cohomology of permutation representations

Article copyright:
© Copyright 1974
American Mathematical Society