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On base sizes for actions of finite classical groups

On base sizes for actions of finite classical groups
On base sizes for actions of finite classical groups
Let G be a finite almost simple classical group and let ? be a faithful primitive non-standard G-set. A base for G is a subset B C_ ? whose pointwise stabilizer is trivial; we write b(G) for the minimal size of a base for G. A well-known conjecture of Cameron and Kantor asserts that there exists an absolute constant c such that b(G) ? c for all such groups G, and the existence of such an undetermined constant has been established by Liebeck and Shalev. In this paper we prove that either b(G) ? 4, or G = U6(2).2, G? = U4(3).22 and b(G) = 5. The proof is probabilistic, using bounds on fixed point ratios.
0024-6107
545-562
Burness, Timothy C.
a3b369f0-16f5-41e6-84d9-5a50f027bcd6
Burness, Timothy C.
a3b369f0-16f5-41e6-84d9-5a50f027bcd6

Burness, Timothy C. (2007) On base sizes for actions of finite classical groups. Journal of the London Mathematical Society, 75 (3), 545-562. (doi:10.1112/jlms/jdm033).

Record type: Article

Abstract

Let G be a finite almost simple classical group and let ? be a faithful primitive non-standard G-set. A base for G is a subset B C_ ? whose pointwise stabilizer is trivial; we write b(G) for the minimal size of a base for G. A well-known conjecture of Cameron and Kantor asserts that there exists an absolute constant c such that b(G) ? c for all such groups G, and the existence of such an undetermined constant has been established by Liebeck and Shalev. In this paper we prove that either b(G) ? 4, or G = U6(2).2, G? = U4(3).22 and b(G) = 5. The proof is probabilistic, using bounds on fixed point ratios.

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Submitted date: 21 June 2006
Published date: June 2007

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Local EPrints ID: 46634
URI: https://eprints.soton.ac.uk/id/eprint/46634
ISSN: 0024-6107
PURE UUID: bc56edbb-3862-41c8-93b4-f9511f1c2469

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Date deposited: 09 Jul 2007
Last modified: 14 Aug 2019 17:47

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Author: Timothy C. Burness

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