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

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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( 1), for which the first Ritt theorem fails to be true.

Original languageEnglish
Pages (from-to)1-24
Number of pages24
JournalProceedings of the London Mathematical Society
Volume102
Issue number1
DOIs
StatePublished - 1 Jan 2011

ASJC Scopus subject areas

  • Mathematics (all)

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