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The cohomology of the symmetric groups


Author: Benjamin Michael Mann
Journal: Trans. Amer. Math. Soc. 242 (1978), 157-184
MSC: Primary 55F40; Secondary 18H10
DOI: https://doi.org/10.1090/S0002-9947-1978-0500961-9
MathSciNet review: 0500961
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Abstract: Let $ {{\mathcal{S}}_n}$ be the symmetric group on n letters and SG the limit of the sets of degree +1 homotopy equivalences of the $ n - 1$ sphere. Let p be an odd prime. The main results of this paper are the calculations of $ {H^{\ast}}({\mathcal{S}_n},\,Z/p)$ and $ {H^{\ast}}(SG,Z/p)$ as algebras, determination of the action of the Steenrod algebra, $ \mathcal{a}(p)$, on $ {H^{\ast}}({\mathcal{S}_n},\,Z/p)$ and $ {H^{\ast}}(SG,Z/p)$ and integral analysis of $ {H^{\ast}}({\mathcal{S}_n},\,Z,\,p)$ and $ {H^{\ast}}(SG,\,Z,\,p)$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1978-0500961-9
Keywords: Cohomology of groups, classifying spaces, Steenrod algebra
Article copyright: © Copyright 1978 American Mathematical Society

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