A CHARACTERIZATION OF PROJECTIVE SPECIAL LINEAR GROUP L\(_3\)(5) BY nse - Liu, Shitian (Italian Journal of Pure and Applied Mathematics, 2014)
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, the authors proved that the groups L3(2) and L3(4) are unique determined by nse. In this paper, we prove that if G is a group such that nse(G) = nse(L3(5)), then G \(\cong\) L3(5).