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.
545-562
Burness, Timothy C.
a3b369f0-16f5-41e6-84d9-5a50f027bcd6
June 2007
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), .
(doi:10.1112/jlms/jdm033).
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: http://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: 15 Mar 2024 09:25
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Author:
Timothy C. Burness
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