Transitive Permutation Groups with Bounded Movement

PERMUTATION GROUPS WITH BOUNDED MOVEMENT ATTAINING THE BOUNDS FOR ODD PRIMES

Let G be a transitive permutation group on a set ? and let m be a positive integer. If no element of G moves any subset of ? by more than m points, then |? | [2mp I (p-1)] wherep is the least odd primedividing |G |. When the bound is attained, we show that | ? | = 2 p q ….. q where ? is a non-negative integer with 2 < p, r 1 and q is a prime satisfying p < q < 2p, ? = 0 or 1, I i n....

On Transitive Permutation Groups

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

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.

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(...