Torsion units in integral group rings of metacyclic groups
type: Item
instance of: scholarly article
title: Torsion units in integral group rings of metacyclic groups
zbMATH Open document ID: 0551.16004
DOI: 10.1016/0022-314X(84)90095-7
author: Sudarshan K. Sehgal
author: C. Polcino Milies
published in: Journal of Number Theory
publication date: 1984-01-01T00:00:00Z
review text: The paper contains the first non-trivial result in connection with a striking conjecture going back to Zassenhaus and stating that to each unit of finite order in the integral group ring \({\mathbb{Z}}G\) of a finite group G there exists a group element which, up to a sign, in the rational group algebra \({\mathbb{Q}}G\) is conjugate to the unit in question. The conjecture is confirmed for G being a split extension of a cyclic p-group by a cyclic p'-group with faithful action. Meanwhile it has also been confirmed for less special metacyclic groups [the second author and the reviewer, Math. Ann. 264, 257-270 (1983; Zbl 0521.16006)].
Mathematics Subject Classification ID: 16U60
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 20C05
zbMATH DE Number: 3877369
zbMATH Keywords: unit of finite order
zbMATH Keywords: integral group ring
reviewed by: Jürgen Ritter
MaRDI profile type: Publication
cites work: Torsion units of integral group rings of metacyclic groups
cites work: Q5340151
cites work: Units of integral group rings of metabelian groups
cites work: Q4129579
cites work: The Group of Units of the Integral Group Ring ZS3
cites work: Q4198893
description: scientific article; zbMATH DE number 3877369