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Base sizes for sporadic simple groups

Abstract

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.

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Correspondence to Timothy C. Burness.

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Burness, T.C., O’Brien, E.A. & Wilson, R.A. Base sizes for sporadic simple groups. Isr. J. Math. 177, 307–333 (2010). https://doi.org/10.1007/s11856-010-0048-3

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  • DOI: https://doi.org/10.1007/s11856-010-0048-3

Keywords

  • Conjugacy Class
  • Simple Group
  • Maximal Subgroup
  • Permutation Group
  • Double Coset