On the Nse Characterization of Certain Finite Simple Groups

For a group g, πe(g) and sm(g) are denoted the set of orders of elements and the number of elements of order m in g, respectively. let nse(g) = {sm(g) | m ∈ πe(g)}. an arbitrary finite group m is nse characterization if, for every group g, the equality nse(g) = nse(m) implies that g ∼= m. in this paper, we are going to show that the non- abelian finite simple groups a9, a10, a12, u4(3), u5(2), u6(2), s6(2), o+ 8 (2) and hs are characterizable by nse.