Finite Permutation Groups with Few Orbits Under the Action on the Power Set

Alexander Betz, Max Chao-Haft, Ting Gong, Thomas Michael Keller, Anthony Ter-Saakov, Yong Yang

Published 2019-08-01Version 1

The set-transitive groups acting on an $n$ symbol set (i.e. the groups that have $n+1$ set-orbits) have been classified in \cite{BP55}. In this paper we completely classify the groups with $n+r$ set-orbits for $2 \leq r \leq 5$ as well as lay out a method that allows one to go further.