Transitive Extensions of a Class of Doubly Transitive Groups
نویسندگان
چکیده
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...
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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....
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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...
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ژورنال
عنوان ژورنال: Nagoya Mathematical Journal
سال: 1966
ISSN: 0027-7630,2152-6842
DOI: 10.1017/s002776300001196x