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

M. Muzychuk; F. Pakovich

doi:10.1112/plms/pdq009

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

M. Muzychuk, F. Pakovich

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

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 language	American English
Pages (from-to)	1-24
Number of pages	24
Journal	Proceedings of the London Mathematical Society
Volume	102
Issue number	1
DOIs	https://doi.org/10.1112/plms/pdq009
State	Published - 1 Jan 2011

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1112/plms/pdq009

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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.",

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AB - 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.

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

Abstract

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