On orbital partitions and exceptionality of primitive permutation groups
نویسندگان
چکیده
منابع مشابه
On Orbital Partitions and Exceptionality of Primitive Permutation Groups
Let G and X be transitive permutation groups on a set Ω such that G is a normal subgroup of X. The overgroup X induces a natural action on the set Orbl(G,Ω) of non-trivial orbitals of G on Ω. In the study of Galois groups of exceptional covers of curves, one is led to characterizing the triples (G,X,Ω) where X fixes no elements of Orbl(G,Ω); such triples are called exceptional. In the study of ...
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We give a description of infinite families of finite primitive permutation groups for which there is a uniform finite upper bound on the diameter of all orbital graphs. This is equivalent to describing families of finite permutation groups such that every ultraproduct of the family is primitive. A key result is that, in the almost simple case with socle of fixed Lie rank, apart from very specif...
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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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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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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2004
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-04-03396-3