Base sizes for sporadic simple groups

Tim C Burness, Eamonn O'Brien, Robert Wilson

Research output: Contribution to journalArticle (Academic Journal)peer-review

56 Citations (Scopus)


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) is at most 7, with equality if and only if G is the Mathieu group M_24 in its natural action on 24 points. This settles a conjecture of Cameron.
Original languageEnglish
Pages (from-to)307-334
Number of pages28
JournalIsrael Journal of Mathematics
Publication statusPublished - 2010


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