Trivial units in commutative group rings of \(G\times C_n\)
type: Item
instance of: scholarly article
title: Trivial units in commutative group rings of \(G\times C_n\)
author: Ömer Küsmüş
published in: Algebra and Discrete Mathematics
publication date: 2024-08-12T00:00:00Z
review text: A famous result due to \N\textit{G. Higman} [Proc. Lond. Math. Soc. (2) 46, 231--248 (1940; Zbl 0025.24302)] states that the torsion units of the integral group ring \(\mathbb{Z}G\) of an arbitrary abelian group \(G\) are always trivial being of the form \(\pm G\).\N\NThe article under review is devoted to the study of some special cases of this statement, especially to studying the trivial units in commutative group rings of the group \(G\times C_n\), where \(G\) is an abelian group and \(C_n\) is the standard cyclic group of order \(p^n\) for some \(n\in \mathbb{N}\). The main results are stated and proved Theorems 1, 2, 3 and 4, respectively.
reviewed by: Peter Danchev
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 16U60
zbMATH DE Number: 7895271
zbMATH Keywords: trivial units
zbMATH Keywords: commutative group rings
zbMATH Keywords: direct products
MaRDI profile type: Publication
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DOI: 10.12958/ADM2086
description: scientific article; zbMATH DE number 7895271