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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 ([email protected])
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Abstract

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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