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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Torsion units in integral group rings


Author: Angela Valenti
Journal: Proc. Amer. Math. Soc. 120 (1994), 1-4
MSC: Primary 20C05; Secondary 16S34, 16U60
MathSciNet review: 1186996
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Abstract: Let $ G = \left\langle a \right\rangle \rtimes X$ where $ \left\langle a \right\rangle $ is a cyclic group of order $ n,X$ is an abelian group of order $ m$, and $ (n,m) = 1$. We prove that if $ \mathbb{Z}G$ is the integral group ring of $ G$ and $ H$ is a finite group of units of augmentation one of $ \mathbb{Z}G$, then there exists a rational unit $ \gamma $ such that $ {H^\gamma } \subseteq G$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1186996-9
PII: S 0002-9939(1994)1186996-9
Article copyright: © Copyright 1994 American Mathematical Society