Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-27T21:58:12.937Z Has data issue: false hasContentIssue false
  • English
  • Français

ON TRANSITIVE PERMUTATION GROUPS WITH PRIMITIVE SUBCONSTITUENTS

Published online by Cambridge University Press:  01 May 1999

DMITRII V. PASECHNIK  and
CHERYL E. PRAEGER
DMITRII V. PASECHNIK
Affiliation:
SSOR, Faculty of Technical Mathematics and Informatics, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands
CHERYL E. PRAEGER
Affiliation:
Department of Mathematics, University of Western Australia, Perth, WA 6907, Australia
Get access

Abstract

Let G be a transitive permutation group on a set Ω such that, for ω∈Ω, the stabiliser Gω induces on each of its orbits in Ω\{ω} a primitive permutation group (possibly of degree 1). Let N be the normal closure of Gω in G. Then (Theorem 1) either N factorises as N=GωGδ for some ω, δ∈Ω, or all unfaithful Gω-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 Gω-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 Ω.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 31 , Issue 3 , May 1999 , pp. 257 - 268
Copyright
© The London Mathematical Society 1999

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)