Nse Characterization of the Chevalley group G2(5)

Let G be a group and w(G) = {o(g)│g ∈ G} be the set of element orders of G. Let k ∈ w(G) and sk =│{g ∈ G│o(g) = k}│. Let nse(G) = P{sk│k ∈ ω(G)}. In this paper, we prove that if G is a group and G2(5) is the chevalley simple group of type G2 over GF(5) such that nse(G) = nsae(G2(5)), then G ≡ G2(5).