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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Finite groups of matrices over group rings


Authors: Gerald Cliff and Alfred Weiss
Journal: Trans. Amer. Math. Soc. 352 (2000), 457-475
MSC (1991): Primary 20C10, 20C05; Secondary 16S34, 20H25
DOI: https://doi.org/10.1090/S0002-9947-99-02319-3
Published electronically: July 26, 1999
MathSciNet review: 1608293
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Abstract | References | Similar Articles | Additional Information

Abstract: We investigate certain finite subgroups $\Gamma $ of $GL_{n}(\mathbf{Z}\Pi )$, where $\Pi $ is a finite nilpotent group. Such a group $\Gamma $ gives rise to a $\mathbf{Z}[\Gamma \times \Pi]$-module; we study the characters of these modules to limit the structure of $\Gamma $. We also exhibit some exotic subgroups $\Gamma $.


References [Enhancements On Off] (What's this?)

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Additional Information

Gerald Cliff
Affiliation: Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
Email: gcliff@math.ualberta.ca

Alfred Weiss
Affiliation: Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
Email: aweiss@math.ualberta.ca

DOI: https://doi.org/10.1090/S0002-9947-99-02319-3
Keywords: Finite group, module, character
Received by editor(s): November 1, 1997
Published electronically: July 26, 1999
Additional Notes: This research was supported by grants from the Natural Sciences and Engineering Research Council of Canada.
Article copyright: © Copyright 1999 American Mathematical Society

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