Characters of some finite groups of Lie type with a restriction containing a linear character once.
type: Item
instance of: scholarly article
title: Characters of some finite groups of Lie type with a restriction containing a linear character once.
zbMATH Open document ID: 1123.20009
author: Vahid Dabbaghian-Abdoly
published in: Journal of Algebra
publication date: 2007-04-11T00:00:00Z
review text: Let \(\chi\) be an irreducible character of a finite group \(G\). A subgroup \(H\) of \(G\) is called a \(\chi\)-subgroup if the restriction of \(\chi\) to \(H\) has at least one linear constituent of multiplicity 1. In the paper under review the author considers some finite groups \(G\) of Lie type, i.e. \(\text{Sp}(4,2^f)\), \(G_2(q)\), \(Sz(q)\), \(Re(q)\), and a Sylow \(p\)-subgroup \(H\) of \(G\) where \(q\) is a power of \(p\) or \(p=2\) in the case of the symplectic group, and then determines the irreducible character \(\chi\) of \(G\) such that \(H\) is a \(\chi\)-subgroup of \(G\). The author also determines characters \(\chi\) of \(G\) for which \(H\) is not a \(\chi\)-subgroup.
Mathematics Subject Classification ID: 20C33
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20C40
zbMATH DE Number: 5141729
zbMATH Keywords: finite groups of Lie type
zbMATH Keywords: irreducible characters
zbMATH Keywords: Sylow subgroups
zbMATH Keywords: linear constituents
reviewed by: M. R. Darafsheh
describes a project that uses: REPSN
describes a project that uses: GAP
describes a project that uses: CHEVIE
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2006.10.021
OpenAlex ID: W2083388598
Wikidata QID: Q115351503
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DOI: 10.1016/J.JALGEBRA.2006.10.021
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description: scientific article; zbMATH DE number 5141729