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There exist many characterizations for the sporadic simple groups.In this paper we give two new characterizations for the Mathieusporadic groups. Let M be a Mathieu group and let p be thegreatest prime divisor of |M|. In this paper, we prove that M is uniquely determined by |M| and |NM(P)|, where P∈Sylp(M). Also we prove that if G is a finite group, thenG≅M if and only if for every prime q, |NM(Q)|=|NG(Q′)|, where Q∈Sylq(M) and Q′∈Sylq(G)

Groups with the same orders of Sylow normalizers as the Mathieu groups