On the Orbital Diameter of Primitive Affine Groups

TL;DR

This paper establishes explicit bounds on the orbital diameters of primitive affine groups with almost quasisimple stabilizers and partially classifies those with diameter at most 2.

Contribution

It provides new explicit bounds on orbital diameters and a partial classification for primitive affine groups with small diameters.

Findings

Explicit bounds on orbital diameters for certain primitive affine groups

Partial classification of groups with orbital diameter ≤ 2

Enhanced understanding of the structure of primitive affine groups

Abstract

The orbital diameter of a primitive permutation group is the maximal diameter of its orbital graphs. There has been a lot of interest in bounds for the orbital diameter. In this paper we provide explicit bounds on the diameters of groups of primitive affine groups with almost quasisimple point stabilizer. As a consequence we obtain a partial classification of primitive affine groups with orbital diameter less than or equal to 2.