Hirsch induction and torsion units in group rings
type: Item
instance of: scholarly article
title: Hirsch induction and torsion units in group rings
zbMATH Open document ID: 0823.16021
DOI: 10.1007/BF01197214
author: Z. S. Marciniak
author: Sudarshan K. Sehgal
published in: Archiv der Mathematik
publication date: 1995-10-15T00:00:00Z
review text: We study the torsion of the group of normalized integral units for polycyclic groups. We consider groups for which a \(p\)-local version of Hirsch induction can be applied. We prove that for such groups, as well as for all nilpotent and all metabelian groups, every finite group of units from \(Z \Gamma\) has an isomorphic copy inside \(\Gamma\). We also find new classes of groups with the unique trace property: each torsion unit has only one non vanishing Bass trace and hence may be a conjugate of a group element.
Mathematics Subject Classification ID: 16U60
Mathematics Subject Classification ID: 20F16
Mathematics Subject Classification ID: 20C07
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 20F19
Mathematics Subject Classification ID: 20E07
zbMATH DE Number: 769516
zbMATH Keywords: Zassenhaus conjecture
zbMATH Keywords: group of normalized integral units
zbMATH Keywords: polycyclic groups
zbMATH Keywords: \(p\)-local version of Hirsch induction
zbMATH Keywords: metabelian groups
zbMATH Keywords: finite group of units
zbMATH Keywords: unique trace property
zbMATH Keywords: torsion units
zbMATH Keywords: Bass trace
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01197214
OpenAlex ID: W2027854465
description: scientific article; zbMATH DE number 769516