Jordan-Holder theorem for imprimitivity systems and maximal decompositions of rational functions
Complex Variables
2014-02-26 v2 Algebraic Geometry
Group Theory
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 the automorphism group of the sphere for which the first Ritt theorem fails to be true.
Keywords
Cite
@article{arxiv.0712.3869,
title = {Jordan-Holder theorem for imprimitivity systems and maximal decompositions of rational functions},
author = {M. Muzychuk and F. Pakovich},
journal= {arXiv preprint arXiv:0712.3869},
year = {2014}
}
Comments
In the current version the approach was considerably simplified and a lot of new material was added (see e.g. Section 2.2, Section 2.3 and Section 3.2). On the other hand, some results of rather calculating character were removed