Unit groups of semisimple group algebras of Abelian \(p\)-groups over a field
type: Item
instance of: scholarly article
title: Unit groups of semisimple group algebras of Abelian \(p\)-groups over a field
zbMATH Open document ID: 0876.16021
author: Nako Nachev
author: Todor Mollov
published in: Journal of Algebra
publication date: 1997-12-01T00:00:00Z
review text: Let \(G\) be an abelian \(p\)-group, \(K\) a field of characteristic different from \(p\) and let \(KG\) be the group algebra of \(G\) over \(K\). The authors give a description of the unit group \(U(KG)\) of \(KG\) when \(K\) is a field of the first kind with respect to \(p\) and the first Ulm factor \(G/G^1\) is a direct sum of cyclic groups, or when \(G\) is an arbitrary abelian \(p\)-group, and \(K\) is a field of the second kind with respect to \(p\). The indicated description of \(U(KG)\) extends results of \textit{Z. Chatzidakis} and \textit{P. Pappas} [J. Lond. Math. Soc., II. Ser. 44, No. 1, 9-23 (1991; Zbl 0701.16031)].
Mathematics Subject Classification ID: 16U60
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 20C07
Mathematics Subject Classification ID: 16D60
Mathematics Subject Classification ID: 20K10
zbMATH DE Number: 1013939
zbMATH Keywords: Abelian \(p\)-groups
zbMATH Keywords: group algebras
zbMATH Keywords: unit groups
zbMATH Keywords: direct sums of cyclic groups
reviewed by: S. V. Mihovski
MaRDI profile type: Publication
full work available at URL: jabr.1996.6826
OpenAlex ID: W1969815193
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DOI: 10.1006/JABR.1996.6826
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description: scientific article; zbMATH DE number 1013939