Primitive permutation groups whose subdegrees are bounded above

Simon M. Smith (postdoc '12)

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

ArXiv: 1201.0803