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Base sizes for simple groups and a conjecture of Cameron

By Timothy C. Burness, Martin W. Liebeck and Aner Shalev

Abstract

Let G be a permutation group on a finite set ?. A base for G is a subset B C_ ? whose pointwise stabilizer in G is trivial; we write b(G) for the smallest size of a base for G. In this paper we prove that b(G) ? if G is an almost simple group of exceptional Lie type and is a primitive faithful G-set. An important consequence of this result, when combined with other recent work, is that b(G) ? 7 for any almost simple group G in a non-standard action, proving a conjecture of Cameron. The proof is probabilistic and uses bounds on fixed point ratios

Topics: QA
Year: 2009
OAI identifier: oai:eprints.soton.ac.uk:69937
Provided by: e-Prints Soton

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