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On base sizes for actions of finite classical groups
Author(s) -
Burness Timothy C.
Publication year - 2007
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdm033
Subject(s) - mathematics , conjecture , pointwise , combinatorics , base (topology) , constant (computer programming) , finite group , simple group , finite set , simple (philosophy) , group (periodic table) , discrete mathematics , physics , mathematical analysis , computer science , philosophy , epistemology , quantum mechanics , programming language
Let G be a finite almost simple classical group and let Ω be a faithful primitive non‐standard G ‐set. A subset of Ω is a base for G if its pointwise stabilizer in G is trivial. Let b ( G ) be 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 ) ⩽ slant 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 = U 6 (2) · 2, G ω = U 4 (3) · 2 2 and b ( G ) = 5. The proof is probabilistic, using bounds on fixed point ratios.