A CHARACTERIZATION OF THE GROUP Ap+3 BY ITS NON-COMMUTING GRAPH

Year 2012, Volume: 11 Issue: 11, 160 - 164, 01.06.2012

M. R. Darafsheh P. Yousefzadeh

Abstract

The non-commuting graph ∇(G) of a non-abelian finite group G
is defined as follows: its vertex set is G − Z(G) and two distinct vertices x and
y are joined by an edge if and only if the commutator of x and y is not the
identity. In this paper we prove if G is a finite group with ∇(G) ∼= ∇(Ap+3),
then G ∼= Ap+3, where Ap+3 is the alternating group of degree p + 3, where p
is a prime number.

Keywords

non-commuting graph, alternating group