A New Characterization of some Mathieu Groups by the Number of Sylow Subgroups

Let G be a finite group with trivial center and n_{p}(G) be the number of Sylow p- subgroup of G. In this paper we prove that if n_{p}(G)=n_{p}(M_{n}), for every prime p in pi (G), where n in {11, 12}, then M_{n}<= G <= Aut(M_{n}).