On transitive permutation groups with primitive subconstituents

D.V. Pasechnik, Cheryl Praeger

Research output: Contribution to journalArticle

Abstract

Let G be a transitive permutation group on a set Omega such that, for omega is an element of Omega, the stabiliser G(omega) induces on each of its orbits in Omega\{omega} a primitive permutation group (possibly of degree 1). Let N be the normal closure of G(omega) in G. Then (Theorem 1) either N factorises as N = G(omega)G(delta) for some omega, delta is an element of Omega, or all unfaithful G(omega)-orbits, if any exist, are infinite. This result generalises a theorem of I. M. Isaacs which deals with the case where there is a finite upper bound on the lengths of the G(omega)-orbits. Several further results are proved about the structure of G as a permutation group, focussing in particular on the nature of certain G-invariant partitions of Omega.
Original languageEnglish
Pages (from-to)257-268
JournalBulletin of the London Mathematical Society
Volume31
DOIs
Publication statusPublished - 1999

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