Complex linear groups of degree at most v-3
type: Item
instance of: scholarly article
title: Complex linear groups of degree at most v-3
zbMATH Open document ID: 0595.20051
DOI: 10.1016/0021-8693(85)90158-9
author: Pamela A. Ferguson
published in: Journal of Algebra
publication date: 1985-01-01T00:00:00Z
review text: Let G be a finite group with a faithful irreducible complex character of degree at most p-3 for p a prime greater than 7. The author shows that either G has a normal p-Sylow subgroup or G/Z(G) is isomorphic to PSL(2,p). This was done for \(| Z(G)|\) odd by Feit and for \(\{\) \(| Z(G)| \geq 12\) and \(G=G'\}\) by the author. Harvy Blau has since then generalized this to replacing p by a prime power q where G has a cyclic p-Sylow subgroup of order q. Both Ferguson and Blau use the classification of simple groups in their latest work here.
Mathematics Subject Classification ID: 20G20
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20G40
Mathematics Subject Classification ID: 20D05
zbMATH DE Number: 3957443
zbMATH Keywords: irreducible complex character
zbMATH Keywords: p-Sylow subgroup
MaRDI profile type: Publication
full work available at URL: 0021-8693(85)90158-9
OpenAlex ID: W2068993851
cites work: On finite linear groups of degree 16
cites work: An Inequality for Complex Linear Groups of Small Degree
cites work: On Groups Whose Order Contains a Prime Number to the First Power I
cites work: Q5668957
cites work: Groups which have a faithful representation of degree less than \((p-1)/2\)
cites work: Groups Which Have a Faithful Representation of Degree Less Than p - 1
cites work: On finite linear groups
cites work: Finite linear groups of degree less than p-2
cites work: Q5577154
cites work: On finite simple groups of characteristic 2 type
cites work: Introduction to Lie Algebras and Representation Theory
cites work: The non-abelian simple groups g, |g| < 106— character tables
cites work: p-solvable doubly transitive permutation groups
cites work: Certain embeddings among finite groups of Lie type
cites work: Prime graph components of finite groups
cites work: Finite Groups Having a Faithful Representation of Degree Less Than (2p + 1)/3
description: scientific article; zbMATH DE number 3957443