Integral group rings with Jordan decomposition
type: Item
instance of: scholarly article
title: Integral group rings with Jordan decomposition
zbMATH Open document ID: 0696.16004
DOI: 10.1007/BF01200034
published in: Archiv der Mathematik
publication date: 1991-01-01T00:00:00Z
review text: The authors investigate Jordan decomposition for elements \(x\) of the integral group ring \(\mathbb{Z} G\) of a finite group \(G\). If \(x\) is written as the sum \(s+n\) of commuting elements \(s\) and \(n\) of the rational group algebra \(\mathbb{Q} G\), where \(s\) is semisimple and \(n\) nilpotent, then one says that Jordan decomposition holds in \(\mathbb{Z} G\) if \(s\) and \(n\) necessarily lie in \(\mathbb{Z} G\) for all \(x\) in \(\mathbb{Z} G\). The authors characterize all finite groups \(G\) for which Jordan decomposition holds in \(\mathbb{Z} G\).
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 20C05
zbMATH DE Number: 4139957
zbMATH Keywords: Jordan decompositions
zbMATH Keywords: integral group rings
zbMATH Keywords: commuting elements
author: Inder Bir S. Passi
author: Alfred W. Hales
MaRDI profile type: Publication
cites work: Q5607044
cites work: Q3377733
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cites work: Q4198893
full work available at URL: https://doi.org/10.1007/bf01200034
OpenAlex ID: W2069591772
description: scientific article; zbMATH DE number 4139957