On the nilpotency index of the radical of a group algebra. VI
type: Item
instance of: scholarly article
title: On the nilpotency index of the radical of a group algebra. VI
zbMATH Open document ID: 0596.16010
DOI: 10.1016/0021-8693(85)90188-7
author: Kaoru Motose
published in: Journal of Algebra
publication date: 1985-01-01T00:00:00Z
review text: [For Part V of this series cf. ibid. 90, 251-258 (1984; Zbl 0543.16005); VII, ibid. 101, 299-302 (1986; Zbl 0589.16012).] Let F be a field of characteristic \(p>0\). Let G be a finite p-solvable group with a p-Sylow subgroup P of order \(p^ m\). Let \(M=O_{p'}(G)\), let \(H=O_{p',p}(G)\) and let F/M be the Frattini subgroup of H/M. The main result is that if \(t(G)>p^{m-1}\) and if G is not of p-length 1 then \(p=2\), F/M is cyclic and G/F is the symmetric group of order 24. A very similar result was proved and crucially used by \textit{S. Koshitani} [J. Algebra 94, 106-112 (1985; reviewed above)] but the present proof is less involved.
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 16Nxx
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20C05
zbMATH DE Number: 3959688
zbMATH Keywords: nilpotency index
zbMATH Keywords: finite p-solvable group
zbMATH Keywords: p-Sylow subgroup
zbMATH Keywords: Frattini subgroup
zbMATH Keywords: p-length
MaRDI profile type: Publication
full work available at URL: 0021-8693(85)90188-7
OpenAlex ID: W1986476208
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description: scientific article; zbMATH DE number 3959688