Local units and circular index in abelian \(p\)-group rings
type: Item
instance of: scholarly article
title: Local units and circular index in abelian \(p\)-group rings
zbMATH Open document ID: 0794.16021
DOI: 10.1016/0022-4049(92)90171-B
author: Klaus Hoechsmann
published in: Journal of Pure and Applied Algebra
publication date: 1993-05-16T00:00:00Z
review text: The paper is concerned with units in integral group rings \(\mathbb{Z} A\) of abelian \(p\)-groups \(A\), \(p\neq 2\). First a \(\mathbb{Z}_ p\)-basis of the form \(w_ p(z)\), \(1\neq z\in A\) for \(\{1+ (z-1)+ (z^{-1}-1)\): \(z\in A\} \subset \mathbb{Z}_ p A\) is given, where \(w_ p(x)\) is a certain polynomial over \(\mathbb{Z}_ p\). Then a subgroup \(\Lambda\) in \((\mathbb{Z} A)^ \times\) of a similar structure is built which lies in the group \(\Omega\) of all units appearing circular under every character of \(A\). Finally the index \([\Omega: \Lambda]\) is shown to be the order of a \(D\)-group of ideal classes of \(\mathbb{Z} A\).
reviewed by: Jürgen Ritter
Mathematics Subject Classification ID: 16U60
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 16S34
zbMATH DE Number: 166146
zbMATH Keywords: units in integral group rings
zbMATH Keywords: abelian \(p\)-groups
zbMATH Keywords: circular units
zbMATH Keywords: characters
zbMATH Keywords: \(D\)-groups of ideal classes
MaRDI profile type: Publication
cites work: Q5730966
cites work: On the classgroup of integral grouprings of finite abelian groups
cites work: Q5792522
cites work: Units and class-groups in integral elementary Abelian group rings
cites work: Généralisation d'un Lemme de Kummer
cites work: Logarithms and units in p-adic Abelian group rings
cites work: Constructible units in Abelian p-group rings
cites work: On the projective class group of cyclic groups of prime power order
cites work: Q5612629
cites work: Class Groups of Cyclotomic Fields and Group Rings
cites work: Q3943047
description: scientific article; zbMATH DE number 166146