On Lie metabelian group rings
type: Item
instance of: scholarly article
title: On Lie metabelian group rings
zbMATH Open document ID: 0817.20003
DOI: 10.1007/BF03322289
author: Frank Levin
author: Gerhard Rosenberger
published in: Results in Mathematics
publication date: 1994-12-07T00:00:00Z
review text: For a commutative ring \(R\) in which \(2 \neq 0\) and a finite group \(G\) of order prime to 6 it is shown that each of the properties below implies \(G\) to be abelian. (i) The subring of the group ring \(RG\) which is generated by all \(g + g^{-1}\), \(g \in G\) is Lie metabelian. (ii) The subring generated by all \(g - g^{-1}\) is Lie metabelian.
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 16W10
zbMATH DE Number: 687811
zbMATH Keywords: finite group
zbMATH Keywords: group ring
zbMATH Keywords: Lie metabelian
Wikidata QID: Q115390785
reviewed by: Jürgen Ritter
MaRDI profile type: Publication
cites work: Lie nilpotence of group rings
full work available at URL: https://doi.org/10.1007/bf03322289
OpenAlex ID: W2022434836
description: scientific article; zbMATH DE number 687811