Unitary units in group rings of groups of order \(16\)
type: Item
instance of: scholarly article
title: Unitary units in group rings of groups of order \(16\)
zbMATH Open document ID: 0833.16034
published in: Rocky Mountain Journal of Mathematics
publication date: 1994-09-28T00:00:00Z
review text: Let \(U(ZG)\) denote the group of units of the integral group ring of a finite group \(G\). To give a set of generators of this group is, in general, a difficult problem. As a compromise, it has been a major trend in the area to look for a set of generators of a subgroup of finite index. The so-called bicyclic and Bass cyclic units constitute such a set in many cases. Recently \textit{A. A. Bovdi} and \textit{S. K. Sehgal} [Publ. Mat., Barc. 36, No. 1, 197-204 (1992; Zbl 0778.16013)] have considered groups \(G\) such that all bicyclic units in \(ZG\) are unitary. In particular, there are five non-Hamiltonian groups of order 16 with that property. In this note it is shown that for these five groups, the Bass cyclic and unitary units generate a subgroup of finite index in \(U(ZG)\).
Mathematics Subject Classification ID: 16U60
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 16S34
zbMATH DE Number: 645227
zbMATH Keywords: groups of units
zbMATH Keywords: integral group rings
zbMATH Keywords: finite groups
zbMATH Keywords: generators
zbMATH Keywords: subgroups of finite index
zbMATH Keywords: Bass cyclic units
zbMATH Keywords: bicyclic units
author: M. M. Parmenter
reviewed by: C. Polcino Milies
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181072425
OpenAlex ID: W2089542288
cites work: Unitary subgroup of the multiplicative group of the integral group ring of a cyclic group
cites work: Unitary subgroup of integral group rings
cites work: Describing units of integral group rings of some 2-groups
cites work: Q4022764
cites work: Units of group rings of groups of order 16
cites work: Bicyclic and Bass Cyclic Units in Group Rings
cites work: Q3202255
cites work: Construction of Units in Integral Group Rings of Finite Nilpotent Groups
cites work: Integral Group Rings with Trivial Central Units
cites work: Q4198893
DOI: 10.1216/RMJM/1181072425
description: scientific article; zbMATH DE number 645227