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

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International Electronic Journal of Algebra
Volume:11 Issue:11
A CHARACTERIZATION OF THE GROUP Ap+3 BY ITS NON-COMMUTING GRAPH

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

Authors : M R Darafsheh, P Yousefzadeh

Pages : 160-164

View : 44 | Download : 10

Publication Date : 2012-06-01

Article Type : Research Paper

Abstract :The non-commuting graph ∇insert ignore into journalissuearticles values(G); of a non-abelian finite group G is defined as follows: its vertex set is G − Zinsert ignore into journalissuearticles values(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 ∇insert ignore into journalissuearticles values(G); ∼= ∇insert ignore into journalissuearticles values(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

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