Group algebras with units satisfying an Engel identity
type: Item
instance of: scholarly article
title: Group algebras with units satisfying an Engel identity
zbMATH Open document ID: 1008.16027
DOI: 10.1007/BF02904264
author: David Riley
publication date: 2002-12-17T00:00:00Z
review text: The main result in this paper shows that, for a periodic group \(G\) and a field \(F\) of prime characteristic \(p>0\) the fact that the unit group \(U(FG)\) is \(n\)-Engel, for some \(n\), is equivalent to \(FG\) being \(n\)-Engel, for some \(n\), and that this happens if and only if \(G\) is a nilpotent group containing a normal subgroup \(A\) such that both \(G/A\) and \(A'\) are finite \(p\)-groups. The implication showing that \(FG\) being \(n\)-Engel gives that \(U(FG)\) \(n\)-Engel had already been proved by the present author and \textit{M. C. Wilson} in a more general context [in Proc. Am. Math. Soc. 127, No. 4, 973-976 (1999; Zbl 0915.16023)].
reviewed by: C. Polcino Milies
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 16U60
Mathematics Subject Classification ID: 16R50
Mathematics Subject Classification ID: 20F18
Mathematics Subject Classification ID: 20F45
Mathematics Subject Classification ID: 16W10
zbMATH DE Number: 1846801
zbMATH Keywords: group algebras
zbMATH Keywords: unit groups
zbMATH Keywords: Engel identities
zbMATH Keywords: periodic groups
zbMATH Keywords: nilpotent groups
MaRDI profile type: Publication
cites work: Q3262241
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cites work: Q4198893
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 1846801