Abstract Groups as Doubly Transitive Permutation Groups *

A combinatorial approach to doubly transitive permutation groups

Known doubly transitive permutation groups are well studied and the classification of all doubly transitive groups has been done by applying the classification of the finite simple groups. Readers may refer to [6]. This may mean that it is not still sufficient to study doubly transitive groups as permutation groups. Typical arguments on doubly transitive groups are seen in the book[3]. In the p...

Doubly 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...

Finite permutation groups of rank 3

By the rank of a transitive permutation group we mean the number of orbits of the stabilizer of a point thus rank 2 means multiple transitivity. Interest is drawn to the simply transitive groups of "small" rank > 2 by the fact that every known finite simple group admits a representation as a primitive group of rank at most 5 while not all of these groups have doubly transitive representations. ...

Two 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....

ON DOUBLY TRANSITIVE PERMUTATION GROUPS OF DEGREE n AND ORDER 2p(n-l)n