Hostname: page-component-8448b6f56d-c47g7 Total loading time: 0 Render date: 2024-04-18T16:51:26.548Z Has data issue: false hasContentIssue false
  • English
  • Français

TORSION UNITS IN INTEGRAL GROUP RINGS OF CERTAIN METABELIAN GROUPS

Published online by Cambridge University Press:  28 July 2008

Martin Hertweck
Martin Hertweck
Affiliation:
Universität Stuttgart, Fachbereich Mathematik, IGT, Pfaffenwaldring 57, 70569 Stuttgart, Germany (hertweck@mathematik.uni-stuttgart.de)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is shown that any torsion unit of the integral group ring $\mathbb{Z}G$ of a finite group $G$ is rationally conjugate to an element of $\pm G$ if $G=XA$ with $A$ a cyclic normal subgroup of $G$ and $X$ an abelian group (thus confirming a conjecture of Zassenhaus for this particular class of groups, which comprises the class of metacyclic groups).

Keywords

Primary 16S3416U60Secondary 20C05integral group ringtorsion unitbimoduleZassenhaus conjecture
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 51 , Issue 2 , June 2008 , pp. 363 - 385
Copyright
Copyright © Edinburgh Mathematical Society 2008