Oligomorphic group

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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.[1]


  1. ^ Bhattacharjee, Meenaxi; Macpherson, Dugald; Möller, Rögnvaldur G.; Neumann, Peter M. (1998). Notes on infinite permutation groups. Lecture Notes in Mathematics. 1698. Berlin: Springer-Verlag. p. 83. ISBN 3-540-64965-4. Zbl 0916.20002. 

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