Brauer characters and fields of values
type: Item
instance of: scholarly article
title: Brauer characters and fields of values
zbMATH Open document ID: 1390.20012
author: Dan Rossi
published in: Journal of Group Theory
publication date: 2017-11-06T00:00:00Z
review text: Let \(G\) be a finite group, \(p\) a prime number, and \(\mathbb F\) a subfield of the complex numbers. A \(p\)-regular element \(x\) of a finite group \(G\) is called an \(\mathbb F\)-element iff \(\phi (x)\in \mathbb F\) for every \(p\)-Brauer character \(\phi\) of \(G\). Two results are proved, which are modular analogues of results of \textit{I. M. Isaacs} and \textit{G. Navarro} [J. Group Theory 12, No. 5, 635--650 (2009; Zbl 1186.20009)], as follows. First, if \(N\) is a normal subgroup of \(G\) such that the identity is the only \(p\)-regular \(\mathbb F\)-element of \(N\), then the canonical epimorphism \(G \rightarrow G/N\) induces a bijection between the conjugacy classes of \(p\)-regular \(\mathbb F\)-elements of \(G\) and the conjugacy classes of \(p\)-regular \(\mathbb F\)-elements of \(G/N\). Second, every finite group \(G\) has a unique largest normal subgroup \(N\) such that the identity is the only \(p\)-regular \(\mathbb F\)-element of \(N\). The proof of the injectivity in the first result constitutes the bulk of the work in the paper.
reviewed by: Thomas Michael Keller
Mathematics Subject Classification ID: 20C20
zbMATH DE Number: 6803034
zbMATH Keywords: finite group
zbMATH Keywords: Brauer characters
zbMATH Keywords: \(p\)-regular elements
zbMATH Keywords: conjugacy classes, field of values
MaRDI profile type: Publication
full work available at URL: jgth-2017-0023
OpenAlex ID: W2737009873
cites work: Q5634146
cites work: Q3521460
cites work: Group elements and fields of character values
cites work: On the existence of a complement for a finite simple group in its automorphism group
cites work: Q4387775
cites work: Rational irreducible characters and rational conjugacy classes in finite groups
cites work: Brauer characters and rationality.
DOI: 10.1515/JGTH-2017-0023
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description: scientific article; zbMATH DE number 6803034