Base sizes for sporadic simple groups

@article{Burness2010BaseSF,
  title={Base sizes for sporadic simple groups},
  author={Timothy C. Burness and E. O'Brien and Robert A. Wilson},
  journal={Israel Journal of Mathematics},
  year={2010},
  volume={177},
  pages={307-333}
}
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… Expand

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