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Paper   IPM / M / 7777
School of Mathematics
  Title:   Groups with the same orders of Sylow normalizers as the Mathieu groups
1.  Behr. Khosravi
2.  Behn. Khosravi
  Status:   Published
  Journal: Internat. J. Math. Math. Sci.
  Vol.:  9
  Year:  2005
  Pages:   1449-1453
  Supported by:  IPM
There exist many characterizations for the sporadic simple groups. In this paper we give two new characterizations for the Mathieu sporadic groups. Let M be a Mathieu group and p be the greatest prime advisor of |M|. In this paper, we prove that M is uniquely determined by |M| and |NM(P)|, where PSylp(M). Also, we prove that if G is a finite group, then GM if and only if for every prime q, |NM(Q)|=|NG(Q)|, where QSylq(M) and QSylq(G).

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