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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

Topics:
QA

Year: 2007

OAI identifier:
oai:eprints.soton.ac.uk:46634

Provided by:
e-Prints Soton

Downloaded from
http://dx.doi.org/10.1112/jlms/jdm033

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