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| Paper IPM / M / 8466 |
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| Abstract: | |
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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 G ≅ S if and only of for every prime
q,|NS(Q)|=|NG(Q′)|, where Q ∈
Sylq(S) and Q′ ∈ Sylq(G).
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