Group algebras with centrally metabelian unit groups
type: Item
instance of: scholarly article
title: Group algebras with centrally metabelian unit groups
zbMATH Open document ID: 0869.16024
DOI: 10.5565/PUBLMAT_40296_14
author: Meena Sahai
published in: Publicacions Matemàtiques
publication date: 1997-09-07T00:00:00Z
full work available at URL: https://eudml.org/doc/41264
review text: The paper determines the finite groups \(G\) having the property that the unit group \(U\) of their group algebra \(KG\) over a field \(K\) of positive characteristic \(\neq 2\) is centrally metabelian, meaning that the second derived term \(\delta^2U\) is central in \(U\). This holds, for example, whenever \(KG\) is Lie centrally metabelian (\(G\) may even be infinite), and \textit{M. Sahai} and \textit{J. B. Srivastava} [J. Algebra 187, No. 2, 7-15 (1997)]; \textit{R. K. Sharma} and \textit{J. B. Srivastava} [J. Algebra 151, 476-486 (1992; Zbl 0788.16019)] have provided necessary and sufficient conditions for \(KG\) being so. In the paper under review the full list of groups \(G\) is shown to consist of all abelian \(G\) and, moreover, in characteristic 3, groups \(G\) with commutator subgroup of order 3. The proofs are rather computational.
Mathematics Subject Classification ID: 16U60
Mathematics Subject Classification ID: 16W10
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20F45
Mathematics Subject Classification ID: 20F14
zbMATH DE Number: 999994
zbMATH Keywords: centrally metabelian unit groups
zbMATH Keywords: finite groups
zbMATH Keywords: group algebras
reviewed by: Jürgen Ritter
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 999994