Bounding graph diameters of nonsolvable groups.
type: Item
instance of: scholarly article
title: Bounding graph diameters of nonsolvable groups.
zbMATH Open document ID: 1070.20009
author: John K. McVey
published in: Journal of Algebra
publication date: 2004-11-29T00:00:00Z
review text: For a finite group \(G\) the set of degrees of all the irreducible characters of \(G\) is denoted by \(\text{cd}(G)\). The common-divisor graph \(\Gamma(G)\) associated with \(G\) is a graph with vertices \(\chi(1)\in\text{cd}(G)\) different from 1 and two vertices \(a\) and \(b\) are adjacent if they have a non-trivial common divisor. The author proved [in J. Algebra 280, No. 2, 415-425 (2004; Zbl 1077.20010)] that if \(G\) is a solvable group, then the diameter of \(\Gamma(G)\) is at most \(3\). In the paper under review the author proves the same result for a non-solvable group, extending the same result for every finite group.
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 2119564
zbMATH Keywords: nonsolvable groups
zbMATH Keywords: character degrees
zbMATH Keywords: irreducible characters
zbMATH Keywords: common-divisor graphs
reviewed by: M. R. Darafsheh
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2004.08.019
OpenAlex ID: W4205597829
cites work: Groups having three complex irreducible character degrees
cites work: Q3682663
cites work: Q3684278
cites work: Q5634146
cites work: Endliche Gruppen I
cites work: Q4312077
cites work: A characterization of groups in terms of the degrees of their characters. II
cites work: On blocks of twisted group algebras
cites work: A solvable group whose character degree graph has diameter \(3\)
cites work: Connectedness of degree graphs of nonsolvable groups.
cites work: Diameters 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: Bounding graph diameters of solvable groups.
DOI: 10.1016/J.JALGEBRA.2004.08.019
description: scientific article; zbMATH DE number 2119564