Abstract
AbstractLet 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.
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