This paper describes briefly a theory of Cartesian decompositions of a set Omega that are preserved by a permutation group G on Omega. If G has a transitive minimal normal subgroup M, then there is a one-to-one correspondence between the Cartesian decompositions preserved by G and certain families of subgroups of M, called Cartesian systems. The various types of Cartesian decompositions can be categorised by various types of Cartesian systems. These types are described, and examples of each are given.
|Publication status||Published - 2004|