On the primitive groups of class $3p$

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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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On the Orders of Primitive Permutation Groups

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 res...

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On the Order of Primitive Groups

At the end of a memoir on primitive groups in the first volume of the Bulletin of the Mathematical Society of France, f Jordan announced the following theorem : Let q be a poaitive integer leas than 6, p any prime number greater than q; the degree of a primitive group G that contains a subatitutitm of order p on q cyclea (without including the alternating group) cannot exceed pq + q + 1. The pr...

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ژورنال

عنوان ژورنال: Transactions of the American Mathematical Society

سال: 1905

ISSN: 0002-9947

DOI: 10.1090/s0002-9947-1905-1500692-5