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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
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).

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2008