NSE characterization of the Chevalley group G2(4).

Let G be a group and ω(G) = {o(g)|g ∈ G} be the set of element orders of G. Let k ∈n ω(G) and sk = |{g ∈ G |o(g) = k}|. Let nse(G) = {sk|k ∈ ω(G)}. In this paper, we prove that if G is a group and G2(4) is the Chevalley group such that nse(G) = nse(G2(4)), then G ≅ G2(4). [ABSTRACT FROM AUTHOR]