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On Primitive Linear Representations of Finite Groups

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.

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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.

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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
Record Number:CaltechAUTHORS:20170710-101117286
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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, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78889
Deposited By: Ruth Sustaita
Deposited On:10 Jul 2017 17:27
Last Modified:15 Nov 2021 17:43

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