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 ∈ {L ₄(7), L ₄(11), L ₄(13), L ₄(16), L ₄(17)} and G is a finite group such that ∇(G) ≅ ∇(L), then G ≅ L.

Keywords

noncommuting graph / spectrum / prime graph / projective special linear group L ₄(q) / recognition by noncommuting graph

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