Recognition by noncommuting graph of finite simple groups L 4(q)

Abstract

Let G be a nonabelian group. We define the noncommuting graph ∇(G) of G as follows: its vertex set is G\Z(G), the set of non-central elements of G, and two different vertices x and y are joined by an edge if and only if x and y do not commute as elements of G, i.e., [x, y] ≠ 1. We prove that if L ∈ {L4(7), L4(11), L4(13), L4(16), L4(17)} and G is a finite group such that ∇(G) ≅ ∇(L), then G ≅ L.