On a theorem of Broline
type: Item
instance of: scholarly article
title: On a theorem of Broline
zbMATH Open document ID: 0930.20006
author: Lászlo Héthelyi
author: K. Corrádi
published in: Journal of Algebra
publication date: 2000-02-09T00:00:00Z
review text: The following addition to Broline's Theorem is given [see \textit{I. M. Isaacs}, Character theory of finite groups, New York, Academic Press (1976; Zbl 0337.20005), Theorem 12.24]: Theorem. Let \(\chi\) be an irreducible character of a finite group \(G\), \(\ker(\chi)\leq F\vartriangleleft G\) such that \(F/\ker(\chi)\) is nilpotent. If \((|F:\ker(\chi)|,\chi(1))=1\) and \(F\) is nonnilpotent, then there exists \(\psi\in\text{Irr}(G)\) such that \(\psi(1)>\chi(1)\) and \(\ker(\psi)<\ker(\chi)\).
Mathematics Subject Classification ID: 20C15
zbMATH DE Number: 1247583
zbMATH Keywords: Broline's theorem
zbMATH Keywords: irreducible characters
zbMATH Keywords: finite groups
reviewed by: Yakov Berkovich
MaRDI profile type: Publication
full work available at URL: jabr.1998.7554
OpenAlex ID: W2012798989
cites work: Nilpotence and character kernels
cites work: Q4103728
DOI: 10.1006/JABR.1998.7554
description: scientific article; zbMATH DE number 1247583