Real characters of \(p'\)-degree.
type: Item
instance of: scholarly article
title: Real characters of \(p'\)-degree.
zbMATH Open document ID: 1080.20007
author: I. M. Isaacs
author: Gunter Malle
author: Gabriel Navarro
published in: Journal of Algebra
publication date: 2004-10-01T00:00:00Z
review text: The authors prove the following theorems using the Glauberman correspondence and the classification of simple groups: Theorem A. Let \(G\) be a finite group and suppose that \(p\neq 3\) is prime. If \(G\) is nonsolvable, then it has a nonprincipal, real, irreducible character of \(p'\)-degree. If \(G\) is solvable, then it has such a character if and only if \(|N_G(P)|\) is even, where \(P\in\text{Syl}_p(G)\). Theorem B. Suppose that \(G\) is a finite \(p\)-solvable group, where \(p\) is prime. Then \(G\) has a nonprincipal, real-valued, irreducible character of \(p'\)-degree if and only if \(|N_G(P)|\) is even, where \(P\in\text{Syl}_p(G)\).
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D05
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 2105346
zbMATH Keywords: Glauberman correspondence
zbMATH Keywords: Clifford correspondence
zbMATH Keywords: Gallagher theorem
zbMATH Keywords: Steinberg characters
zbMATH Keywords: nonsolvable groups
zbMATH Keywords: finite \(p\)-solvable groups
zbMATH Keywords: real-valued irreducible characters
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2003.09.032
OpenAlex ID: W1997055363
cites work: Q3684278
cites work: Q3907722
cites work: Q4321756
cites work: Q4312077
cites work: Q3481947
cites work: Torsion in reductive groups
cites work: Q4296491
DOI: 10.1016/J.JALGEBRA.2003.09.032
description: scientific article; zbMATH DE number 2105346