Semiprimitivity of group algebras of locally finite groups. II
type: Item
instance of: scholarly article
title: Semiprimitivity of group algebras of locally finite groups. II
zbMATH Open document ID: 0856.16024
DOI: 10.1016/0022-4049(95)00069-0
published in: Journal of Pure and Applied Algebra
publication date: 1997-02-12T00:00:00Z
review text: The result of this paper is an intermediate contribution to the author's project to obtain a criterion (in group terms) of semiprimitivity of the group algebra of a locally finite group [for part I cf. the author and the reviewer, Proc. Lond. Math. Soc., III. Ser. 67, No. 2, 243-276 (1993; Zbl 0798.16015)]. In this paper the author considers the locally finite groups that have a finite subnormal series with factors which are either infinite simple, or generated by locally subnormal subgroups or contain no element of order \(p\). Let \(K\) be a field of characteristic \(p\). The main theorem says that the group algebra \(K[G]\) is semiprimitive (i.e. the Jacobson radical of \(K[G]\) is 0) if and only if \(G\) contains no locally subnormal subgroup of order a multiple of \(p\). (A finite subgroup \(X\) of \(G\) is called locally subnormal if \(X\) is subnormal in every finite subgroup containing \(X\)).
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 20E32
Mathematics Subject Classification ID: 20C07
Mathematics Subject Classification ID: 20E25
Mathematics Subject Classification ID: 16D60
Mathematics Subject Classification ID: 20F14
Mathematics Subject Classification ID: 20F50
zbMATH DE Number: 908494
zbMATH Keywords: semiprimitivity
zbMATH Keywords: group algebras
zbMATH Keywords: locally finite groups
zbMATH Keywords: finite subnormal series
zbMATH Keywords: locally subnormal subgroups
zbMATH Keywords: Jacobson radical
author: D. S. Passman
MaRDI profile type: Publication
full work available at URL: 0022-4049(95)00069-0
OpenAlex ID: W2101060950
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description: scientific article; zbMATH DE number 908494