  In this paper we prove several results about the lattice of imprimitivity
systems of a permutation group containing a cyclic subgroup with at most two
orbits. As an application we generalize the first Ritt theorem about functional
decompositions of polynomials, and some other related results. Besides, we
discuss examples of rational functions, related to finite subgroups of the
automorphism group of the sphere for which the first Ritt theorem fails to be
true.
