Finite solvable groups whose character graphs are trees.
type: Item
instance of: scholarly article
title: Finite solvable groups whose character graphs are trees.
zbMATH Open document ID: 1118.20012
author: Yi-Tao Wu
author: Pu Zhang
published in: Journal of Algebra
publication date: 2007-04-18T00:00:00Z
review text: For a finite group \(G\), the character graph \(\Gamma(G)\) has the nonlinear irreducible complex characters as its vertices, and two of them are joined by an edge whenever their degrees have a common prime divisor. -- This graph has been studied quite extensively in recent years. In the paper under review it is shown that for solvable groups, \(\Gamma(G)\) has no triangles if and only if \(\Gamma(G)\) has only two vertices, or \(G\) is isomorphic to the symmetric group \(S_4\). The condition of having no triangles is also equivalent to \(\Gamma(G)\) being a tree.
reviewed by: Thomas Michael Keller
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 20D10
zbMATH DE Number: 5144423
zbMATH Keywords: finite groups
zbMATH Keywords: character degree graphs
zbMATH Keywords: trees
zbMATH Keywords: irreducible complex characters
zbMATH Keywords: symmetric group \(S_4\)
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2006.09.009
OpenAlex ID: W2030873907
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DOI: 10.1016/J.JALGEBRA.2006.09.009
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description: scientific article; zbMATH DE number 5144423