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Constructing Representations of Finite Simple Groups and Covers

Published online by Cambridge University Press:  20 November 2018

Vahid Dabbaghian-Abdoly
Vahid Dabbaghian-Abdoly*
Affiliation:
Centre for Experimental and Constructive Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, BC V5A 1S6 email: vdabbagh@cecm.sfu.ca
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Abstract

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Let $G$ be a finite group and $\chi $ be an irreducible character of $G$ . An efficient and simple method to construct representations of finite groups is applicable whenever $G$ has a subgroup $H$ such that $\chi H$ has a linear constituent with multiplicity 1. In this paper we show (with a few exceptions) that if $G$ is a simple group or a covering group of a simple group and $\chi $ is an irreducible character of $G$ of degree less than 32, then there exists a subgroup $H$ (often a Sylow subgroup) of $G$ such that $\chi H$ has a linear constituent with multiplicity 1.

Keywords

20C4020C1group representationssimple groupscentral coversirreducible representations

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 58 , Issue 1 , 01 February 2006 , pp. 23 - 38
Copyright
Copyright © Canadian Mathematical Society 2006

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