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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Hypercentral units in integral group rings


Authors: Yuanlin Li and M. M. Parmenter
Journal: Proc. Amer. Math. Soc. 129 (2001), 2235-2238
MSC (2000): Primary 16S34, 20C07
Published electronically: January 23, 2001
MathSciNet review: 1823905
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Abstract:

In this note, we show that when $G$ is a torsion group the second center of the group of units $U({\mathbb Z}G)$ of the integral group ring ${\mathbb Z}G$ is generated by its torsion subgroup and by the center of $U({\mathbb Z}G)$. This extends a result of Arora and Passi (1993) from finite groups to torsion groups, and completes the characterization of hypercentral units in ${\mathbb Z}G$ when $G$ is a torsion group.


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Additional Information

Yuanlin Li
Affiliation: Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, New Foundland, Canada A1C 5S7

M. M. Parmenter
Affiliation: Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, New Foundland, Canada A1C 5S7

DOI: https://doi.org/10.1090/S0002-9939-01-05848-8
Received by editor(s): August 3, 1999
Received by editor(s) in revised form: December 24, 1999
Published electronically: January 23, 2001
Additional Notes: This research was supported in part by grants from the Natural Sciences and Engineering Research Council.
Communicated by: Steven D. Smith
Article copyright: © Copyright 2001 American Mathematical Society