Israel Journal of Mathematics

, Volume 177, Issue 1, pp 307-333

Base sizes for sporadic simple groups

  • Timothy C. BurnessAffiliated withSchool of Mathematics, University of Southampton Email author 
  • , E. A. O’BrienAffiliated withDepartment of Mathematics, University of Auckland
  • , Robert A. WilsonAffiliated withSchool of Mathematical Sciences, Queen Mary, University of London

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Let G be a permutation group acting on a set Ω. A subset of Ω is a base for G if its pointwise stabilizer in G is trivial. We write b(G) for the minimal size of a base for G. We determine the precise value of b(G) for every primitive almost simple sporadic group G, with the exception of two cases involving the Baby Monster group. As a corollary, we deduce that b(G) ⩽ 7, with equality if and only if G is the Mathieu group M24 in its natural action on 24 points. This settles a conjecture of Cameron.