On primitive $2$-closed permutation groups of rank at most four

Abstract

We characterise the primitive 2-closed groups $G$ of rank at most four that are not the automorphism group of a graph or digraph and show that if the degree is at least 2402 then there are just two infinite families or $G⩽\mathrm{A}\Gamma {\mathrm{L}}_1(p^d)$, the 1-dimensional affine semilinear group. These are the first known examples of non-regular 2-closed groups that are not the automorphism group of a graph or digraph.

References in corpus (1)

• On the Automorphism Group of a Graph

Cited by in corpus (1)

• New 2-closed groups that are not automorphism groups of digraphs