On the O'Nan-Scott theorem for finite primitive permutation groups
نویسندگان
چکیده
منابع مشابه
Closures of Finite Primitive Permutation Groups
Let G be a primitive permutation group on a finite set ft, and, for k ^ 2, let G be the Ar-closure of G, that is, the largest subgroup of Sym (ft) preserving all the G-invariant ^-relations on ft. Suppose that G<H^ G and G and H have different socles. It is shown that k ^ 5 and the groups G and H are classified explicitly.
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We study the minimal non-trivial subdegrees of finite primitive permutation groups that admit an embedding into a wreath product in product action, giving a connection with the same quantity for the primitive component. We discover that the primitive groups of twisted wreath type exhibit different (but interesting) behaviour from the other primitive types. 2000 Mathematics Subject Classificatio...
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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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Let G be a permutation group acting on a set V . A partition π of V is distinguishing if the only element of G that fixes each cell of π is the identity. The distinguishing number of G is the minimum number of cells in a distinguishing partition. We prove that if G is a primitive permutation group and |V | ≥ 336, its distinguishing number is two.
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
سال: 1988
ISSN: 0263-6115
DOI: 10.1017/s144678870003216x