On the Orders of Primitive Permutation Groups
نویسندگان
چکیده
The problem of bounding the order of a permutation group G in terms of its degree n was one of the central problems of 19th century group theory (see [4]). It is closely related to the 1860 Grand Prix problem of the Paris Academy, but its history goes in fact much further back (see e.g. [3], [1] and [10]). The heart of the problem is of course the case where G is a primitive group. The best result here is due
منابع مشابه
On The Orders of Primitive Groups
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 applicat...
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