THE AUTOMORPHISM GROUP OF COMMUTING GRAPH OF A FINITE GROUP

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 51, Issue 4, 2014, pp.1145-1153
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2014.51.4.1145

Title & Authors

THE AUTOMORPHISM GROUP OF COMMUTING GRAPH OF A FINITE GROUP

Mirzargar, Mahsa; Pach, Peter P.; Ashrafi, A.R.;

Mirzargar, Mahsa; Pach, Peter P.; Ashrafi, A.R.;

Abstract

Let G be a finite group and X be a union of conjugacy classes of G. Define C(G,X) to be the graph with vertex set X and () joined by an edge whenever they commute. In the case that X = G, this graph is named commuting graph of G, denoted by . The aim of this paper is to study the automorphism group of the commuting graph. It is proved that Aut() is abelian if and only if ; is of prime power if and only if , and is square-free if and only if . Some new graphs that are useful in studying the automorphism group of are presented and their main properties are investigated.

Keywords

commuting graph;automorphism group;extra special group;

Language

English

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