Finite groups with real-valued irreducible characters of prime degree.
type: Item
instance of: scholarly article
title: Finite groups with real-valued irreducible characters of prime degree.
zbMATH Open document ID: 1176.20007
author: Silvio Dolfi
author: Emanuele Pacifici
author: Lucia Sanus
published in: Journal of Algebra
publication date: 2008-10-22T00:00:00Z
full work available at URL: http://hdl.handle.net/2434/53090
review text: Let \(G\) be a finite group and \(\text{cd}_{\text{rv}}(G)\) be the degrees of all the real-valued irreducible characters of \(G\). The authors prove the following: If every real-valued nonlinear irreducible character of \(G\) has prime degree then -- \(G\) is solvable. -- \(\text{cd}_{\text{rv}}(G)\subseteq\{1,2,p\}\), where \(p\) is an odd prime. -- \(l_2(G)\leqslant 2\) and \(l_{2'}(G)\leqslant 1\). They also consider the more general situation in which the real-valued irreducible characters of a finite group have all squarefree degree.
reviewed by: Vahid Dabbaghian
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 5355735
zbMATH Keywords: real characters
zbMATH Keywords: character degrees
zbMATH Keywords: real-valued irreducible characters
MaRDI profile type: Publication
OpenAlex ID: W1997559675
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DOI: 10.1016/J.JALGEBRA.2008.06.002
description: scientific article; zbMATH DE number 5355735