JORDAN-HÖLDER THEOREM FOR IMPRIMITIVITY SYSTEMS AND MAXIMAL DECOMPOSITIONS OF RATIONAL FUNCTIONS
Mikhail E. Muzychuk, Fedor Pakovich · 2012
Abstract. 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 Aut(CP 1), for which the first Ritt theorem fails to be true. 1.