On odd degree parts of cohomology of sporadic simple groups whose Sylow \(p\)-subgroup is the extra-special \(p\)-group of order \(p^3\)
type: Item
instance of: scholarly article
title: On odd degree parts of cohomology of sporadic simple groups whose Sylow \(p\)-subgroup is the extra-special \(p\)-group of order \(p^3\)
zbMATH Open document ID: 0910.20035
author: Nobuaki Yagita
published in: Journal of Algebra
publication date: 1999-02-04T00:00:00Z
review text: Let \(p\) be an odd prime and \(G\) be a sporadic simple group whose Sylow \(p\)-subgroups are isomorphic to the extraspecial \(p\)-group \(E=p_+^{1+2}\) of order \(p^3\) and of exponent \(p\). The cohomology ring \(H^*(G;F_p)\) is a subring of \(H^*(E;F_p)\). \textit{M. Tezuka} and \textit{N. Yagita} [J. Algebra 183, No. 2, 483-513 (1996; Zbl 0855.20045)] computed \(H^{\text{even}}(G)_{(p)}\) for all sporadic groups \(G\) whose Sylow \(p\)-subgroups are \(E\). In this paper, the author computes \(H^*(G;F_p)\) by studying its \(H^{\text{even}}(G)_{(p)}\)-module structure.
Mathematics Subject Classification ID: 20J06
Mathematics Subject Classification ID: 20D08
zbMATH DE Number: 1214106
zbMATH Keywords: cohomology of finite groups
zbMATH Keywords: sporadic simple groups
zbMATH Keywords: cohomology rings
reviewed by: Anatoli Kondrat'ev
MaRDI profile type: Publication
full work available at URL: jabr.1997.7251
OpenAlex ID: W2036619154
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DOI: 10.1006/JABR.1997.7251
description: scientific article; zbMATH DE number 1214106