Primitive permutation groups whose subdegrees are bounded above

Abstract

If $G$ is a group of permutations of a set $Ω$ and $α\in Ω$, then the {\em $α$-suborbits} of $G$ are the orbits of the stabilizer $G_α$ on $Ω$. The cardinality of an $α$-suborbit is called a {\em subdegree} of $G$. If the only $G$-invariant equivalence classes on $Ω$ are the trivial and universal relations, then $G$ is said to be a {\em primitive} group of permutations of $Ω$. In this paper we determine the structure of all primitive permutation groups whose subdegrees are bounded above by a finite cardinal number.