A note on degrees of irreducible \(\pi\)-Brauer characters.
type: Item
instance of: scholarly article
title: A note on degrees of irreducible \(\pi\)-Brauer characters.
zbMATH Open document ID: 1162.20009
author: Yanjun Liu
author: Xueling Song
published in: Archiv der Mathematik
publication date: 2009-01-29T00:00:00Z
review text: Let \(G\) be a finite \(\pi\)-separable group where \(\pi\) is a set of primes. Isaacs and others have developed a theory of Brauer characters with respect to \(\pi\). The authors prove: (1) \(G\) has a normal Hall \(\pi\)-subgroup if and only if every irreducible \(\pi\)-Brauer character of \(G\) has \(\pi'\)-degree. (2) If \(G\) has an Abelian \(\pi\)-complement then every irreducible \(\pi\)-Brauer character of \(G\) has \(\pi\)-degree. (3) \(|G|_{\pi'}\leq\sum_{\varphi\in\text{IBr}_\pi(G)}\varphi(1)^2\), with equality if and only if \(G\) has a normal Hall \(\pi\)-subgroup. These results are analogs of known results for the classical case where \(\pi\) consists of a single prime \(p\).
reviewed by: Burkhard Külshammer
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 5500574
zbMATH Keywords: irreducible Brauer characters
zbMATH Keywords: Fong characters
zbMATH Keywords: \(\pi\)-separable groups
zbMATH Keywords: Hall subgroups
zbMATH Keywords: character degrees
MaRDI profile type: Publication
full work available at URL: s00013-008-2816-4
OpenAlex ID: W2065670665
DOI: 10.1007/S00013-008-2816-4
description: scientific article; zbMATH DE number 5500574