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| Paper IPM / M / 7777 |
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| Abstract: | |||||
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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 P ∈ Sylp(M). Also, we prove that if G is a finite group, then
G ≅ M if and only if for every prime q,
|NM(Q)|=|NG(Q′)|, where Q ∈ Sylq(M) and
Q′ ∈ Sylq(G).
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