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Paper   IPM / M / 8466
School of Mathematics
  Title:   Two new characterizations for sporadic simple groups
  Author(s):  Behr. Khosravi (Joint with A. Khosravi)
  Status:   Published
  Journal: Pure Math. Appl.
  Vol.:  16
  Year:  2005
  Pages:   287-293
  Supported by:  IPM
In this paper we give two new characterizations for the sporadic simple groups, based on the orders of the normalizers of the Sylow subgroups. Let S be a sporadic simple group and p be the greatest prime divisor of |S|. In this paper we prove that S is uniquely determined among finite groups by |S| and |NS(P)|, where P ∈ Syl p(S). Also we prove that if G is a finite group. then GS if and only of for every prime q,|NS(Q)|=|NG(Q′)|, where Q ∈ Sylq(S) and Q′ ∈ Sylq(G).

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