Units and class-groups in integral elementary Abelian group rings
type: Item
instance of: scholarly article
title: Units and class-groups in integral elementary Abelian group rings
zbMATH Open document ID: 0628.16008
DOI: 10.1016/0022-4049(87)90050-8
published in: Journal of Pure and Applied Algebra
publication date: 1987-01-01T00:00:00Z
review text: Assume A to be an elementary abelian p-group with p odd. The group of units in \({\mathbb{Z}}A\) having augmentation 1 and being invariant under the canonical involution on \({\mathbb{Z}}A\) is closely related to the product of the corresponding unit groups of \({\mathbb{Z}}C\), C varying over all cyclic subgroups, and also of \({\mathbb{Z}}K\), K varying over all cyclic factor groups. The main result of the paper is concerned with those units of \({\mathbb{Z}}A\) which cannot be written as products of ``cyclic'' units; there are no such, if p is regular, but for irregular, semi-regular p such units exist.
Mathematics Subject Classification ID: 16U60
Mathematics Subject Classification ID: 16S34
zbMATH DE Number: 4021376
zbMATH Keywords: elementary abelian p-group
zbMATH Keywords: group of units
author: Klaus Hoechsmann
reviewed by: Jürgen Ritter
MaRDI profile type: Publication
full work available at URL: 0022-4049(87)90050-8
OpenAlex ID: W2054367265
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description: scientific article; zbMATH DE number 4021376