Israel Journal of Mathematics

, Volume 177, Issue 1, pp 307–333

Base sizes for sporadic simple groups

  • Timothy C. Burness
  • E. A. O’Brien
  • Robert A. Wilson

DOI: 10.1007/s11856-010-0048-3

Cite this article as:
Burness, T.C., O’Brien, E.A. & Wilson, R.A. Isr. J. Math. (2010) 177: 307. doi:10.1007/s11856-010-0048-3


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.

Copyright information

© Hebrew University Magnes Press 2010

Authors and Affiliations

  • Timothy C. Burness
    • 1
  • E. A. O’Brien
    • 2
  • Robert A. Wilson
    • 3
  1. 1.School of MathematicsUniversity of SouthamptonSouthamptonUK
  2. 2.Department of MathematicsUniversity of AucklandAucklandNew Zealand
  3. 3.School of Mathematical Sciences, Queen MaryUniversity of LondonLondonUK