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Construction of central units in integral group rings of finite groups


Authors: Eric Jespers and M. M. Parmenter
Journal: Proc. Amer. Math. Soc. 140 (2012), 99-107
MSC (2010): Primary 16S34, 16U60, 16U70
DOI: https://doi.org/10.1090/S0002-9939-2011-10968-7
Published electronically: May 17, 2011
MathSciNet review: 2833521
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Abstract: In this paper we give new constructions of central units that generate a subgroup of finite index in the central units of the integral group ring $ \mathbb{Z} G$ of a finite group. This is done for a very large class of finite groups $ G$, including the abelian-by-supersolvable groups.


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Additional Information

Eric Jespers
Affiliation: Department of Mathematics, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium
Email: efjesper@vub.ac.be

M. M. Parmenter
Affiliation: Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, Newfoundland, A1C 5S7, Canada
Email: mparmen@mun.ca

DOI: https://doi.org/10.1090/S0002-9939-2011-10968-7
Keywords: Group ring, central unit.
Received by editor(s): June 3, 2010
Received by editor(s) in revised form: July 20, 2010, and November 10, 2010
Published electronically: May 17, 2011
Additional Notes: The first author was supported in part by Onderzoeksraad of Vrije Universiteit Brussel and Fonds voor Wetenschappelijk Onderzoek (Belgium)
The second author was supported in part by the Natural Sciences and Engineering Research Council of Canada.
Communicated by: Jonathan I. Hall
Article copyright: © Copyright 2011 American Mathematical Society

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