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Extremely primitive classical groups

Extremely primitive classical groups
Extremely primitive classical groups
A primitive permutation group is said to be extremely primitive if it is not regular and 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 this paper, we determine the examples in the case of almost simple classical groups. They comprise the 2-transitive actions of PSL2(q) and its extensions of degree q + 1, and of Sp2m(2) of degrees 22m-1 ± 2m-1, together with the 3/2-transitive actions of PSL2(q) on cosets of Dq+1, with q+1 a Fermat prime. In addition to these three families, there are four individual examples.
1580-1610
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.
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 classical groups. Journal of Pure and Applied Algebra, 216 (7), 1580-1610. (doi:10.1016/j.jpaa.2011.10.028).

Record type: Article

Abstract

A primitive permutation group is said to be extremely primitive if it is not regular and 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 this paper, we determine the examples in the case of almost simple classical groups. They comprise the 2-transitive actions of PSL2(q) and its extensions of degree q + 1, and of Sp2m(2) of degrees 22m-1 ± 2m-1, together with the 3/2-transitive actions of PSL2(q) on cosets of Dq+1, with q+1 a Fermat prime. In addition to these three families, there are four individual examples.

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e-pub ahead of print date: November 2011
Published date: July 2012
Organisations: Pure Mathematics

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Local EPrints ID: 338304
URI: https://eprints.soton.ac.uk/id/eprint/338304
PURE UUID: 9555c3ea-32ba-4e1e-97a0-fedd415bc21e

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Date deposited: 14 May 2012 10:43
Last modified: 30 Jul 2018 16:31

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