On elements of prime order in primitive permutation groups
نویسندگان
چکیده
منابع مشابه
Prime order derangements in primitive permutation groups
Let G be a transitive permutation group on a finite set Ω of size at least 2. An element of G is a derangement if it has no fixed points on Ω. Let r be a prime divisor of |Ω|. We say that G is r-elusive if it does not contain a derangement of order r, and strongly r-elusive if it does not contain one of r-power order. In this note we determine the r-elusive and strongly r-elusive primitive acti...
متن کاملPrimitive coherent configurations: On the order of uniprimitive permutation groups
These notes describe the author’s elementary graph theoretic proof of the nearly tight exp(4 √ n ln n) bound on the order of primitive, not doubly transitive permutation groups (Ann. Math., 1981 ). The exposition incorporates a lemma by V. N. Zemlyachenko that simplifies the proof. The central concept in the proof is primitive coherent configurations, a combinatorial relaxation of the action of...
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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.
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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Let G be a transitive permutation group of degree n. We say that G is 2′elusive if n is divisible by an odd prime, but G does not contain a derangement of odd prime order. In this paper we study the structure of quasiprimitive and biquasiprimitive 2′-elusive permutation groups, extending earlier work of Giudici and Xu on elusive groups. As an application, we use our results to investigate autom...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1979
ISSN: 0021-8693
DOI: 10.1016/0021-8693(79)90111-x