RECOGNIZING CHEVALLEY GROUPS \(G_2(q)\) BY nse

Abstract

Let G₂(q) be a Chevalley group over a finite field K= F_q of characteristic p.  For a group G, let nse(G) = {s_k | k ∈ ω(G)} where ω(G) is the set of element orders of G and s_k is the number of elements of order k in G. In this note, we give a new characterization of some special Chevalley groups G₂(q) by nse.