Transitive Permutation Groups with Bounded Movement Having Maximal Degree

The Transitive Permutation Groups of Degree 32

We describe our successful computation of a list of representatives of the 2 801 324 conjugacy classes of transitive groups of degree 32.

Transitive Permutation Groups of Prime-Squared Degree

We explicitly determine all of the transitive groups of degree p2, p a prime, whose Sylow p-subgroup is not isomorphic to the wreath product Z p Z p . Furthermore, we provide a general description of the transitive groups of degree p2 whose Sylow p-subgroup is isomorphic to Z p Z p , and explicitly determine most of them. As applications, we solve the Cayley Isomorphism problem for Cayley objec...

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