Norms and traces in p-adic Abelian group rings
type: Item
instance of: scholarly article
title: Norms and traces in p-adic Abelian group rings
zbMATH Open document ID: 0651.16008
DOI: 10.1007/BF01194153
published in: Archiv der Mathematik
publication date: 1988-01-01T00:00:00Z
review text: The paper under review is to be seen as a further step in the direction of describing integral group ring units in the abelian case in terms of those of the cyclic subgroups. Denote by \(U'_*A\) the subgroup of units in \((1+\Delta_*A)'\) where \(\Delta\) (A) is the augmentation ideal in the p-adic group ring \({\mathbb{Z}}_ pA\) of an abelian p-group A; the * indicates that we only worry about elements that are invariant under \(a\mapsto a^{-1}\) (a\(\in A)\), the ' indicates that we restrict ourselves to looking at the elements having G-norm 1 with G being the automorphism group of \({\mathbb{Z}}/p^ m\) where \(p^ m=\exp A\). Theorem: \(U'_*(A)\) is generated by all \(U'_*(C)\), C running through the cyclic subgroups of A, and \(U'_*(A)\to U'_*(A/B)\) is surjective for any \(B\leq A\). The paper pursues work started already by the author and the reviewer [in Arch. Math. 49, 23-28 (1987; Zbl 0649.16011)] and the author and \textit{S. K. Sehgal} [in J. Number Theory 30, No.3, 375-381 (1988; Zbl 0654.16006)].
Mathematics Subject Classification ID: 16U60
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20C11
zbMATH DE Number: 4061440
zbMATH Keywords: integral group ring units
zbMATH Keywords: augmentation ideal
zbMATH Keywords: p-adic group ring
zbMATH Keywords: abelian p-group
zbMATH Keywords: automorphism group
zbMATH Keywords: cyclic subgroups
author: Klaus Hoechsmann
reviewed by: Jürgen Ritter
MaRDI profile type: Publication
cites work: Logarithms and units in p-adic Abelian group rings
cites work: Units in regular Abelian p-group rings
cites work: Q3714149
description: scientific article; zbMATH DE number 4061440