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Extremely primitive sporadic and alternating groups

Extremely primitive sporadic and alternating groups
Extremely primitive sporadic and alternating groups
A non-regular primitive permutation group is said to be extremely primitive if a point stabilizer acts primitively on each of its orbits. By a theorem of Mann and the second and third authors, every finite extremely primitive group is either almost simple or of affine type. In a recent paper, we classified the extremely primitive almost simple classical groups, and in this note we determine the examples with a sporadic or alternating socle. We obtain two infinite families for An (or Sn); they comprise the natural 2-primitive action of n points, plus the action on partitions of {1,?…?, n} into subsets of size n/2 (with n/2 odd). There are twenty examples for sporadic groups, including the rank 6 representation of Co2 on the cosets of McL.
0024-6093
1-8
Burness, Timothy C.
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Praeger, Cheryl E.
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Seress, Akos
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Burness, Timothy C.
a3b369f0-16f5-41e6-84d9-5a50f027bcd6
Praeger, Cheryl E.
031f04c5-6206-4602-8d50-6be9cd3fd7f3
Seress, Akos
15779de9-d88c-4cd3-8e62-0a32fe8890b3

Burness, Timothy C., Praeger, Cheryl E. and Seress, Akos (2012) Extremely primitive sporadic and alternating groups. Bulletin of the London Mathematical Society, 1-8. (doi:10.1112/blms/bds038).

Record type: Article

Abstract

A non-regular primitive permutation group is said to be extremely primitive if a point stabilizer acts primitively on each of its orbits. By a theorem of Mann and the second and third authors, every finite extremely primitive group is either almost simple or of affine type. In a recent paper, we classified the extremely primitive almost simple classical groups, and in this note we determine the examples with a sporadic or alternating socle. We obtain two infinite families for An (or Sn); they comprise the natural 2-primitive action of n points, plus the action on partitions of {1,?…?, n} into subsets of size n/2 (with n/2 odd). There are twenty examples for sporadic groups, including the rank 6 representation of Co2 on the cosets of McL.

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e-pub ahead of print date: 16 April 2012
Organisations: Pure Mathematics

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Local EPrints ID: 338305
URI: https://eprints.soton.ac.uk/id/eprint/338305
ISSN: 0024-6093
PURE UUID: 981dea2c-f4ac-4b02-b893-7e37844f1e6e

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Date deposited: 14 May 2012 10:48
Last modified: 28 Oct 2019 21:16

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