A NEW CHARACTERIZATION OF PSL(2; 25)

Abstract. Let G be a finite group and _ e(G) be the set of element orders of G. Let k ?  e_(G) and mk be the number of elements of order k in G. Set nse(G):= {mk|k e(G)}. In this paper, we prove that if G is a group such that nse(G)=nse(PSL(2;25)), then G = PSL(2; 25).