Subdegree growth rates of infinite primitive permutation groups

Suborbits in Infinite Primitive Permutation Groups

For every infinite cardinal κ, we construct a primitive permutation group which has a finite suborbit paired with a suborbit of size κ. This answers a question of Peter M. Neumann.

Distinguishing Primitive Permutation Groups

Let G be a permutation group acting on a set V . A partition π of V is distinguishing if the only element of G that fixes each cell of π is the identity. The distinguishing number of G is the minimum number of cells in a distinguishing partition. We prove that if G is a primitive permutation group and |V | ≥ 336, its distinguishing number is two.

Factorizations of Primitive Permutation Groups

Primitive rank 3 groups with a prime subdegree

As a continuation of the study of rank 3 permutation groups G begun in [4] we consider in this paper primitive rank 3 groups of even order in which the stabilizer Ga of a point a has an orbit of prime length. We show in particular that if G has no regular normal subgroup then the minimal normal subgroup M of G is a simple group of rank 3 and the constituent of 214, on the orbit of prime length ...

Infinite Permutation Groups