Generators of large subgroups of the unit group of integral group rings
type: Item
instance of: scholarly article
title: Generators of large subgroups of the unit group of integral group rings
zbMATH Open document ID: 0802.16025
DOI: 10.1007/BF02599315
author: Eric Jespers
author: Guilherme Leal
published in: Manuscripta Mathematica
publication date: 1994-12-13T00:00:00Z
full work available at URL: https://eudml.org/doc/155810
review text: Pursuing work of the reviewer and \textit{S. K. Sehgal} [e.g. Trans. Am. Math. Soc. 324, No. 2, 603-621 (1991; Zbl 0723.16016)], the authors prove that the Bass-Milnor units and the bicyclic units generate a subgroup of finite index in the whole unit group of the integral group ring \(\mathbb{Z} G\) of a finite group \(G\), provided that \(G\) is not from some exceptional list consisting of certain groups of even order. The main new contribution of the paper consists in the construction of a non-trivial idempotent in a given simple component of the rational group algebra \(\mathbb{Q} G\).
Mathematics Subject Classification ID: 16U60
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 20E07
zbMATH DE Number: 492765
zbMATH Keywords: Bass-Milnor units
zbMATH Keywords: bicyclic units
zbMATH Keywords: subgroups of finite index
zbMATH Keywords: unit groups
zbMATH Keywords: integral group rings
zbMATH Keywords: finite groups
zbMATH Keywords: idempotents
zbMATH Keywords: rational group algebras
reviewed by: Jürgen Ritter
MaRDI profile type: Publication
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OpenAlex ID: W2051371396
description: scientific article; zbMATH DE number 492765