Unitary subgroup of the multiplicative group of the integral group ring of a cyclic group
type: Item
instance of: scholarly article
title: Unitary subgroup of the multiplicative group of the integral group ring of a cyclic group
zbMATH Open document ID: 0632.16010
DOI: 10.1007/BF01137668
published in: Mathematical Notes
publication date: 1987-01-01T00:00:00Z
review text: Let U(ZG) be the multiplicative group of the integral group ring ZG of a cyclic group G, where \(| G| =2^{kt}\) (k\(\geq 1)\). If \(f: G\to U(Z)\) is a homomorphism, then the element \(u=\sum_{g\in G}\alpha_ gg\in U(ZG)\) is called f-unitary if \(u^{-1}=u^ f=\sum_{g\in G}\alpha_ gf(g)g^{-1}\) or \(u^{-1}=-u^ f\). The subgroup \(U_ f(ZG)\) of all f-unitary elements of U(ZG) is called the f-unitary subgroup of U(ZG). In this paper the author continues his research on the structure of the subgroup \(U_ f(ZG)\) when f(G)\(\neq \{1\}\) and \(t>1\).
Mathematics Subject Classification ID: 16U60
Mathematics Subject Classification ID: 16S34
zbMATH DE Number: 4027694
zbMATH Keywords: multiplicative group
zbMATH Keywords: integral group ring
zbMATH Keywords: cyclic group
zbMATH Keywords: f-unitary elements
zbMATH Keywords: f-unitary subgroup
author: Adalbert Bovdi
reviewed by: S. V. Mihovski
MaRDI profile type: Publication
cites work: Q3724495
cites work: Q4749965
cites work: The Dirichlet unit theorem, induced characters, and Whitehead groups of finite groups
full work available at URL: https://doi.org/10.1007/bf01137668
OpenAlex ID: W2050944259
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description: scientific article; zbMATH DE number 4027694