منابع مشابه
On a Class of Doubly Transitive Groups1
This theorem is related to a result of Hall [2, Theorem 5.6], which states that if a group G satisfies condition (i) above and in addition either (i') W. is finite, or (i") for some ¿, j'GSDi there is at most one element of G mapping i into j which displaces all of the letters, then G is isomorphic to the group of affine transformations, x—>ax-\-b, a^O, on a near-field. A near-field is an algeb...
متن کاملDoubly transitive 2–factorizations *
Let F be a 2–factorization of the complete graph Kv admitting an automorphism group G acting doubly transitively on the set of vertices. The vertex–set V (Kv) can then be identified with the point–set of AG(n, p) and each 2–factor of F is the union of p–cycles which are obtained from a parallel class of lines of AG(n, p) in a suitable manner, the group G being a subgroup of AGL(n, p) in this ca...
متن کاملTwo Theorems on Doubly Transitive Permutation Groups
In a series of papers [3, 4 and 5] on insoluble (transitive) permutation groups of degree p = 2q +1, where p and q are primes, N. Ito has shown that, apart from a small number of exceptions, such a group must be at least quadruply transitive. One of the results which he uses is that an insoluble group of degree p = 2q +1 which is not doubly primitive must be isomorphic to PSL (3, 2) with p = 7....
متن کاملDoubly Transitive but Not Doubly Primitive Permutation Groups
The connection between doubly transitive permutation groups G on a finite set Cl which are not doubly primitive and automorphism groups of block designs in which X = 1 has been investigated by Sims [2] and Atkinson [1]. If, for a e Q, Ga has a set of imprimitivity of size 2 then it is easy to show that G is either sharply doubly transitive or is a group of automorphisms of a non-trivial block d...
متن کاملDoubly Transitive Permutation Groups Which Are Not Doubly Primitive
Hypothesis (A): G is a doubly transitive permutation group on a set Q. For 01 E Q, G, has a set Z = {B, , B, ,..., B,}, t > 2, which is a complete set of imprimitivity blocks on Q {a}. Let j Bi / = b > 1 for all i. Denote by H the kernel of G, on .Z and by Ki and K< the subgroups of G, fixing Bi setwise and pointwise respectively, 1 .< i < t. Let /3 E Bl . Here j Q j = 1 + ht. M. D. Atkinson ha...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 2007
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788700036880