On multiply transitive permutation groups

Permutation Groups with Multiply - Transitive Suborbits , Ii

In a previous paper with the same title [1], I considered the following situation; G is a primitive, not doubly transitive permutation group on Q, in which the stabiliser G a of a point a acts doubly transitively on an orbit F(a), where |F(a)| = v. Manning [3] showed that, if v > 2, then G a has an orbit larger than F(a). Indeed, with A = F* o T (see [1] for notation), it is easy to see that A(...

On Transitive Permutation Groups

We assign names and new generators to the transitive groups of degree up to 15, reflecting their structure.

Multiply Transitive Substitution Groups*

A substitution group G of degree n is said to be r-fold transitive if each of the n(n — 1) • • • (n—r + 1) permutations of its n letters taken r at a time is represented by at least one substitution of G. It is not sufficient to say that each of its possible sets of r letters is transformed into every one of these sets by the substitutions of G. For instance, in each of the semi-metacyclic grou...

Generating Transitive Permutation Groups

Constructing transitive permutation groups

This paper presents a new algorithm to classify all transitive subgroups of the symmetric group up to conjugacy. It has been used to determine the transitive groups of degree up to 30.