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 ∈ ω ( G ) and s k = | { g ∈ G | o ( g ) = k } | . Let n s e ( G ) = { s k | k ∈ ω ( G ) } . In this paper, we prove that if G is a group and G 2 ( 4 ) is the Chevalley group such that n s e ( G ) = n s e ( G 2 ( 4 ) ) , then G ≅ G 2 ( 4 ) .