On transitive permutation groups with primitive subconstituents
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 unfaith...
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sg-ntu-dr.10356-801152023-02-28T19:28:25Z On transitive permutation groups with primitive subconstituents Pasechnik, Dmitrii V. Praeger, Cheryl E. School of Physical and Mathematical Sciences 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. Accepted version 2013-02-19T04:14:36Z 2019-12-06T13:41:00Z 2013-02-19T04:14:36Z 2019-12-06T13:41:00Z 1999 1999 Journal Article Pasechnik, D. V., & Praeger, C. E. (1999). On Transitive Permutation Groups with Primitive Subconstituents. Bulletin of the London Mathematical Society, 31(3), 257-268. https://hdl.handle.net/10356/80115 http://hdl.handle.net/10220/9150 10.1112/S0024609398005669 en Bulletin of the London Mathematical Society © 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 [http://dx.doi.org/10.1112/S0024609398005669]. application/pdf |
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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. |
| author2 |
School of Physical and Mathematical Sciences |
| author_facet |
School of Physical and Mathematical Sciences Pasechnik, Dmitrii V. Praeger, Cheryl E. |
| format |
Article |
| author |
Pasechnik, Dmitrii V. Praeger, Cheryl E. |
| spellingShingle |
Pasechnik, Dmitrii V. Praeger, Cheryl E. On transitive permutation groups with primitive subconstituents |
| author_sort |
Pasechnik, Dmitrii V. |
| title |
On transitive permutation groups with primitive subconstituents |
| title_short |
On transitive permutation groups with primitive subconstituents |
| title_full |
On transitive permutation groups with primitive subconstituents |
| title_fullStr |
On transitive permutation groups with primitive subconstituents |
| title_full_unstemmed |
On transitive permutation groups with primitive subconstituents |
| title_sort |
on transitive permutation groups with primitive subconstituents |
| publishDate |
2013 |
| url |
https://hdl.handle.net/10356/80115 http://hdl.handle.net/10220/9150 |
| _version_ |
1759853008769777664 |