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Title: On transitive permutation groups with primitive subconstituents
Authors: Pasechnik, Dmitrii V.
Praeger, Cheryl E.
Issue Date: 1999
Source: Pasechnik, D. V., & Praeger, C. E. (1999). On Transitive Permutation Groups with Primitive Subconstituents. Bulletin of the London Mathematical Society, 31(3), 257-268.
Series/Report no.: Bulletin of the London Mathematical Society
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.
DOI: 10.1112/S0024609398005669
Schools: School of Physical and Mathematical Sciences 
Rights: © 1999 London Mathematical Society. This is the author created version of a work that has been peer reviewed and accepted for publication by Bulletin of the London Mathematical Society, London Mathematical Society. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: DOI [].
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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