Oligomorphic group

In group theory, a branch of mathematics, an oligomorphic group is a particular kind of permutation group. If a group G acts on a set S (usually infinite), then G is said to be oligomorphic if this action has only finitely many orbits on every Cartesian product Sⁿ of S (n-tuples of elements of S for every natural number n). The interest in oligomorphic groups is partly based on their application to model theory, e.g. automorphisms in countably categorical theories.