### 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 language | English |
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Pages (from-to) | 257-268 |

Journal | Bulletin of the London Mathematical Society |

Volume | 31 |

DOIs | |

Publication status | Published - 1999 |

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## Cite this

Pasechnik, D. V., & Praeger, C. (1999). On transitive permutation groups with primitive subconstituents.

*Bulletin of the London Mathematical Society*,*31*, 257-268. https://doi.org/10.1112/S0024609398005669