Actions and invariant character degrees. III
type: Item
instance of: scholarly article
title: Actions and invariant character degrees. III
zbMATH Open document ID: 0895.20004
author: Gabriel Navarro
author: Antonio Beltrán
published in: Journal of Algebra
publication date: 1998-09-22T00:00:00Z
review text: This paper is a sequel to two papers of the second author [published in J. Algebra 160, No. 1, 172-178 (1993; Zbl 0805.20007) and ibid. 184, No. 2, 397-406 (1996; Zbl 0868.20004)]. Among others, the following is shown. Theorem A: Suppose the finite group \(A\) acts coprimely on a finite \(\pi\)-separable group \(G\); let \(H\) and \(K\) be an \(A\)-invariant Hall \(\pi\)-subgroup and a \(\pi\)-complement of \(G\), respectively. Then every \(A\)-invariant irreducible character of \(H\) extends to \(G\) if and only if \(C_G(A)\) normalizes \(K\). Theorem D (Same assumptions as before): Every \(A\)-invariant irreducible character of \(G\) has \(\pi\)-degree if and only if \(C_G(A)\) normalizes \(K\) and \(C_K(A)=1\).
reviewed by: Robert W. van der Waall
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D40
Mathematics Subject Classification ID: 20D45
zbMATH DE Number: 1019688
zbMATH Keywords: \(\pi\)-factorable characters
zbMATH Keywords: Fong characters
zbMATH Keywords: finite \(\pi\)-separable groups
zbMATH Keywords: Hall subgroups
zbMATH Keywords: \(\pi\)-complements
zbMATH Keywords: finite groups
zbMATH Keywords: irreducible characters
MaRDI profile type: Publication
full work available at URL: jabr.1996.6914
OpenAlex ID: W4213130120
cites work: A characteristic class of characters of finite \(\pi\)-separable groups
cites work: Characters of \(\pi\)-separable groups
cites work: Fong characters in \(\pi\)-separable groups
cites work: Induction and Restriction of π-Special Characters
cites work: Q4312077
cites work: Actions and invariant character degrees
cites work: Actions and invariant character degrees. II
DOI: 10.1006/JABR.1996.6914
description: scientific article; zbMATH DE number 1019688