Automorphisms and normal subgroups of linear groups.
type: Item
instance of: scholarly article
title: Automorphisms and normal subgroups of linear groups.
zbMATH Open document ID: 1159.20023
DOI: 10.1134/S0001434607090143
author: A. A. Yadchenko
published in: Mathematical Notes
publication date: 2008-09-03T00:00:00Z
review text: An automorphism of prime order \(p\) of a finite group \(G\) is called `coprime' if \(p\) does not divide the order of \(G\). Assume now that \(G\) admits a faithful irreducible complex character of degree \(n\) which is invariant under such an automorphism. Then there are some relations between \(p,n\), and the structure of Sylow subgroups of \(G\).
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 20D45
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 5319852
zbMATH Keywords: finite linear groups
zbMATH Keywords: Sylow subgroups
zbMATH Keywords: Hall subgroups
zbMATH Keywords: coprime automorphisms
zbMATH Keywords: irreducible characters
reviewed by: L. N. Vaserstein
MaRDI profile type: Publication
cites work: On the structure of certain p-solvable linear groups
cites work: Complex p-solvable linear groups
cites work: On finite solvable linear groups
cites work: Q4103728
cites work: Correspondences of Characters for Relatively Prime Operator Groups
cites work: Q3828182
description: scientific article; zbMATH DE number 5319852