Constructing units in commutative group rings
type: Item
instance of: scholarly article
title: Constructing units in commutative group rings
zbMATH Open document ID: 0773.16016
DOI: 10.1007/BF02567067
author: Klaus Hoechsmann
published in: Manuscripta Mathematica
publication date: 1993-01-16T00:00:00Z
full work available at URL: https://eudml.org/doc/155706
review text: Let \(A\) be a finite Abelian group and \(U(A)\) be the unit group of the integral group ring \(\mathbb{Z} A\). In 1965 Bass constructed generators for a free Abelian subgroup of finite index in \(U(A)\). In 1990 Hoechsmann and Ritter described another such construction with the advantage of producing subgroups of much lower index in \(U(A)\), but the disadvantage of being constrained to \(p\)-groups \(A\) of odd order. This paper extends the second procedure to arbitrary \(A\), and clarifies its relation to the first one.
Mathematics Subject Classification ID: 16U60
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 16S34
zbMATH DE Number: 91445
zbMATH Keywords: finite Abelian group
zbMATH Keywords: unit group
zbMATH Keywords: integral group ring
zbMATH Keywords: free Abelian subgroup of finite index
reviewed by: Todor Mollov
MaRDI profile type: Publication
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cites work: Local units and circular index in abelian \(p\)-group rings
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cites work: Q3943047
description: scientific article; zbMATH DE number 91445