Jordan-Holder 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 the automorphism group of the sphere for which the first Ritt theorem fails to be true.
Original languageEnglish GB
Pages (from-to)1-24
JournalProceedings of the London Mathematical Society
Volume102
Issue number1
StatePublished - 2007

Keywords

  • Mathematics - Complex Variables
  • Mathematics - Algebraic Geometry
  • Mathematics - Group Theory
  • 20E15
  • 30D05

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