Aschbacher, Michael (2000) On Primitive Linear Representations of Finite Groups. Journal of Algebra, 234 (2). pp. 627-640. ISSN 0021-8693. doi:10.1006/jabr.2000.8532. https://resolver.caltech.edu/CaltechAUTHORS:20170710-101117286
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Abstract
Let F be a field, let G be a finite group, and let π be a linear representation of G over F; that is, π is a group homomorphism π: G → GL(V) of G into the general linear group on a finite-dimensional vector space V over F. We say π is AI if π is completely reducible and for each normal subgroup H of G, each irreducible FH-submodule of V is absolutely irreducible. For example, if F is algebraically closed then all completely reducible representations over F are AI. In particular, all of our theorems hold over the complex numbers without the hypothesis that the representation is AI.
Item Type: | Article | |||||||||
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Additional Information: | © 2000 Academic Press. Received 12 April 2000. This work was partially supported by National Science Foundation grant NSF-9901367. | |||||||||
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Issue or Number: | 2 | |||||||||
DOI: | 10.1006/jabr.2000.8532 | |||||||||
Record Number: | CaltechAUTHORS:20170710-101117286 | |||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170710-101117286 | |||||||||
Official Citation: | Michael Aschbacher, On Primitive Linear Representations of Finite Groups, Journal of Algebra, Volume 234, Issue 2, 15 December 2000, Pages 627-640, ISSN 0021-8693, https://doi.org/10.1006/jabr.2000.8532. (http://www.sciencedirect.com/science/article/pii/S0021869300985326) | |||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
ID Code: | 78889 | |||||||||
Collection: | CaltechAUTHORS | |||||||||
Deposited By: | Ruth Sustaita | |||||||||
Deposited On: | 10 Jul 2017 17:27 | |||||||||
Last Modified: | 15 Nov 2021 17:43 |
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