In group theory, a branch of mathematics, an oligomorphic group is a particular kind of (usually infinite) permutation group. If a group G acts on a set S, then G is said to be oligomorphic if every Cartesian product, Sn of S has finitely many orbits under the action of G. The interest in oligomorphic group is partly based on their application to model theory, e.g. automorphisms in countably categorical theories.[1]