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.
References

Cameron, Peter J. (1990). Oligomorphic permutation groups. London Mathematical Society Lecture Note Series 152. Cambridge: Cambridge University Press. ISBN 0-521-38836-8. Zbl 0813.20002. 

External links

Oligomorphic permutation groups - Isaac Newton Institute preprint, Peter J. Cameron
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