Diameters of degree graphs of nonsolvable groups.
type: Item
instance of: scholarly article
title: Diameters of degree graphs of nonsolvable groups.
zbMATH Open document ID: 1100.20014
author: Mark L. Lewis
author: Donald L. White
published in: Journal of Algebra
publication date: 2005-04-07T00:00:00Z
review text: Let \(G\) be a finite group. The character degree graph \(\Delta(G)\) is the graph whose vertices are the primes dividing at least one irreducible complex character degree of \(G\) and whose edges are between primes whose product divides at least one such degree. This graph has been studied in quite some detail in the recent past. In the paper under review, the authors are concerned with the diameter of \(\Delta(G)\) (which is the maximum of the diameters of the connected components of \(\Delta(G)\)). They prove that it is bounded above by 2 for nonabelian finite simple groups, except for the Janko group \(J_1\), for which it is 3. They also prove that for an arbitrary finite group the diameter is bounded above by 4; they conjecture, however, that 3 is the best possible upper bound.
reviewed by: Thomas Michael Keller
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20C34
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 2153354
zbMATH Keywords: character degree graphs
zbMATH Keywords: diameters
zbMATH Keywords: first Janko group
zbMATH Keywords: irreducible complex characters
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2004.08.025
OpenAlex ID: W1972380803
cites work: Q3682663
cites work: Q3684278
cites work: Q5634146
cites work: The characters of the finite symplectic group Sp(4,q), q=2\(^f\)
cites work: Q4103728
cites work: On blocks of twisted group algebras
cites work: Connectedness of degree graphs of nonsolvable groups.
cites work: On the Number of Components of a Graph Related to Character Degrees
cites work: Q3834224
cites work: Q4273959
cites work: The Character Tables for SL(3, q), SU(3, q2), PSL(3, q), PSU(3, q2)
cites work: The Characters of the Finite Symplectic Group Sp(4,q)
cites work: The Representations of GL(3,q), GL(4,q), PGL(3,q), and PGL(4,q)
cites work: Degree Graphs of Simple Groups of Exceptional Lie Type
DOI: 10.1016/J.JALGEBRA.2004.08.025
description: scientific article; zbMATH DE number 2153354