On The Orders of Primitive Groups
نویسنده
چکیده
Almost all primitive permutation groups of degree n have order at most n · Q[log2 n]−1 i=0 (n − 2) < n2 , or have socle isomorphic to a direct power of some alternating group. The Mathieu groups, M11, M12, M23 and M24 are the four exceptions. As a corollary the sharp version of a theorem of Praeger and Saxl is established, where M12 turns out to be the ”largest” primitive group. For an application a bound on the orders of permutation groups without large alternating composition factors is given. This sharpens a lemma of Babai, Cameron, Pálfy and generalizes a theorem of Dixon.
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