A new characterization of L₂(q) by its noncommuting graph

Abstract

Let G be a non-abelian group and associate a non-commuting graph ∇(G) with G as follows: the vertex set of ∇(G) is G\Z(G) with two vertices x and y joined by an edge whenever the commutator of x and y is not the identity. In this short paper we prove that if G is a finite group with ∇(G) ≅ ∇(M), where M = L₂(q) (q = pⁿ, p is a prime), then G ≅ M.

Keywords

non-commuting graph / finite group / centralizer

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