On graphs related to conjugacy classes of groups
type: Item
instance of: scholarly article
title: On graphs related to conjugacy classes of groups
zbMATH Open document ID: 0816.20021
DOI: 10.1007/BF02773678
author: Guy Alfandary
published in: Israel Journal of Mathematics
publication date: 1995-07-18T00:00:00Z
review text: Given a finite group \(G\), the graphs \(\Gamma\) and \(\Gamma^*\) are defined as follows. The graph \(\Gamma\) has the noncentral conjugacy classes in \(G\) as vertices, two classes being adjacent if their sizes are not coprime. The graph \(\Gamma^*\) has the prime divisors of the sizes of conjugacy classes in \(G\) as vertices, where two such divisors are adjacent if they both divide the size of some conjugacy class in \(G\). It is proved that if \(\Gamma^*\) is connected then its diameter is at most 3 (a generalization of a similar result for solvable groups by S. Dolfi). Some bounds on the diameter of \(\Gamma\) are also proved.
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 20D10
zbMATH DE Number: 590939
zbMATH Keywords: finite group
zbMATH Keywords: graphs
zbMATH Keywords: noncentral conjugacy classes
zbMATH Keywords: sizes of conjugacy classes
zbMATH Keywords: solvable groups
zbMATH Keywords: diameter
reviewed by: Vladimir D. Tonchev
MaRDI profile type: Publication
cites work: On a Graph Related to Conjugacy Classes of Groups
cites work: On the Diameter of a Graph Related to Conjugacy Classes of Groups
cites work: Arithmetical conditions on the length of the conjugacy classes of a finite group
cites work: Q5577154
cites work: On Finite Groups with Given Conjugate Types I
cites work: Q3663513
cites work: Q3941589
description: scientific article; zbMATH DE number 590939