Feit numbers and \(p'\)-degree characters
type: Item
instance of: scholarly article
title: Feit numbers and \(p'\)-degree characters
zbMATH Open document ID: 1371.20007
author: Carolina Vallejo Rodríguez
published in: Journal of Group Theory
publication date: 2016-11-07T00:00:00Z
full work available at URL: https://arxiv.org/abs/1512.07434
reviewed by: M. R. Darafsheh
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20D10
zbMATH DE Number: 6648181
zbMATH Keywords: Feit number
zbMATH Keywords: solvable group
MaRDI profile type: Publication
OpenAlex ID: W2547401411
Wikidata QID: Q114052962
arXiv ID: 1512.07434
cites work: On a question of Feit concerning character values of finite solvable groups
cites work: Q3901677
cites work: A characteristic class of characters of finite \(\pi\)-separable groups
cites work: Characters of Solvable and Symplectic Groups
cites work: Primitive characters, normal subgroups, and M-groups
cites work: Characters of \(\pi\)-separable groups
cites work: Induction and Restriction of π-Special Characters
cites work: Q3413656
cites work: Induction of characters and \(p\)-subgroups
DOI: 10.1515/JGTH-2016-0011
review text: Let \(G\) be a finite group and \(X\) an irreducible character of \(G\). The Feit number of \(X\) is the smallest integer \(n\) such that the field of values of \(X\) is contained in the \(n\)th cylotomic field \(Q_n\). The Feit conjecture states that if \(G\) is a finite group and \(X\) is an irreducible character of \(G\) there is a \(g\) in \(G\) whose order is the Feit number of \(X\). The conjecture is still open, but it is proved for solvable groups by \textit{G. Amit} and \textit{D. Chillag} in [Pac. J. Math. 122, 257--261 (1986; Zbl 0558.20008)]. In the paper under review, the author shows: NEWLINENEWLINENEWLINELet \(G\) be a finite solvable group and \(p\) be a prime number and \(X\) be an irreducible character of \(G\) with odd degree. Then there exists an element g in \(N_G(P) /_P'\) whose order equals the Feit number of \(X\), where \(P\) is a Sylow \(p\)-subgroup of \(G\).
description: scientific article; zbMATH DE number 6648181