On the orders of primitive linear P'-groups
نویسندگان
چکیده
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...
متن کاملOn 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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چکیده ندارد.
15 صفحه اولON THE ORDERS OF GENERATORS OF CAPABLE p-GROUPS
A group is called capable if it is a central factor group. For each prime p and positive integer c, we prove the existence of a capable p-group of class c minimally generated by an element of order p and an element of order p 1+⌊ c−1 p−1 ⌋ . This is best possible.
متن کامل6 Countable Primitive Linear Groups
We give a complete characterization of countable primitive groups in several settings including linear groups, subgroups of mapping class groups, groups acting minimally on trees and convergence groups. The latter category includes as a special case Kleinian groups as well as subgroups of word hyperbolic groups. As an application we calculate the Frattini subgroup in many of these settings, oft...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1993
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700015951