Characters with stable irreducible constituents
type: Item
instance of: scholarly article
title: Characters with stable irreducible constituents
zbMATH Open document ID: 0839.20013
DOI: 10.1016/S0021-8693(05)80005-5
author: Gabriel Navarro
published in: Journal of Algebra
publication date: 1996-06-11T00:00:00Z
review text: Let \(G\) be a finite group and \(A\) a group of automorphisms of \(G\) which acts on \(G\) coprimely. The author proves the following properties of ordinary irreducible \(A\)-invariant characters: (1) If \(H\) is an \(A\)-invariant subgroup of \(G\) and \(\chi\in \text{Irr} (G)\) is \(A\)-invariant then \(\chi_H\) contains some \(A\)-invariant irreducible constituent. (2) If \(H\) is an \(A\)-invariant subgroup of \(G\) and \(\theta\in \text{Irr} (H)\) is \(A\)-invariant, then \(\theta^G\) contains some \(A\)-invariant irreducible constituent. (3) If \(\alpha\) and \(\beta\) are irreducible \(A\)-invariant characters of \(G\), then \(\alpha \beta\) contains some \(A\)-invariant irreducible constituent.
Mathematics Subject Classification ID: 20C15
zbMATH DE Number: 763196
zbMATH Keywords: finite groups
zbMATH Keywords: groups of automorphisms
zbMATH Keywords: ordinary irreducible characters
zbMATH Keywords: irreducible constituents
MaRDI profile type: Publication
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full work available at URL: s0021-8693(05)80005-5
OpenAlex ID: W2025004053
description: scientific article; zbMATH DE number 763196