A characterization of projective special unitary group U3(5) by nse

Let G be a group and ω(G) be the set of element orders of G. Let k ∈ ω(G) and sk be the number of elements of order k in G. Let nse(G) = {sk∣k ∈ ω(G)}. In Khatami et al. and Liu’s works L3(2) and L3(4) are unique determined by nse(G). In this paper, we prove that if G is a group such that nse(G) = nse(U3(5)), then G ≅ U3(5).