On the nilpotency index of the radical of a group algebra. V
type: Item
instance of: scholarly article
title: On the nilpotency index of the radical of a group algebra. V
zbMATH Open document ID: 0543.16005
DOI: 10.1016/0021-8693(84)90212-6
author: Kaoru Motose
published in: Journal of Algebra
publication date: 1984-01-01T00:00:00Z
review text: [For part IV cf. Math. J. Okayama Univ. 25, 35-42 (1983; Zbl 0514.16007).] Let K be a field of characteristic \(p>0\), let G be a finite p-solvable group, let J(KG) be the radical of the group algebra KG over K and let t(G) be the nilpotency index of J(KG). Mainly by direct calculation the author proves that if \(p=3\) and if G has a 3-Sylow subgroup of the type \(<x,y,c| \quad c^ 3=x^ 3=y^ 3=1,\quad x^ c=x,\quad y^ c=xy,\quad x^ y=x>\) then \(t(G)=9\). This settles a question, left open for \(p=3\), in the work of \textit{S. Koshitani} [J. Algebra 80, 134-144 (1983; Zbl 0507.16011)].
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 16Nxx
Mathematics Subject Classification ID: 20C05
zbMATH DE Number: 3863395
zbMATH Keywords: finite p-solvable group
zbMATH Keywords: radical
zbMATH Keywords: group algebra
zbMATH Keywords: nilpotency index
zbMATH Keywords: 3- Sylow subgroup
MaRDI profile type: Publication
full work available at URL: 0021-8693(84)90212-6
OpenAlex ID: W1991739557
cites work: Q5340151
cites work: Q5577154
cites work: Endliche Gruppen I
cites work: A remark on the nilpotency index of the radical of a group algebra of a p-solvable group
cites work: On the Jacobson radical of a block ideal in a finite p-solvable group for \(p\geq 5\)
cites work: A remark on the Jacobson radical of a block ideal in a finite p-solvable group
cites work: Q5824700
cites work: Q4156548
cites work: Q3659929
cites work: Q3671358
cites work: Radicals of group algebras
cites work: Q5329180
description: scientific article; zbMATH DE number 3863395