NSE characterization of projective special linear group L_3(7)

Let G be a group and ω(G) be the set of element orders of G. Let k ∈ ω(G) and S_k be the number of elements of order k in G. Let nse (G) = {s_k|k ∈ ω(G)}. In Khatami et al and Liu s works, the groups L3(2), L3(4) and L3(5) are unique determined by nse (G). In this paper, we prove that if G is a group such that nse (G)= nse(L_3(7)), then G ∼= L_3(7).