Jordan-Holder theorem for imprimitivity systems and maximal decompositions of rational functions

Details Jordan-Holder theorem for imprimitivity systems and maximal decompositions of rational functions Jordan-Holder theorem for imprimitivity systems and maximal decompositions of rational functions

2007-12-22

arxiv.org/abs/0712.3869v2

Mathematics

Complex Variables

In the current version the approach was considerably simplified and a lot of new material was added (see e.g. Section 2.2, Sec

Scientific paper

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.

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