Base sizes for S-actions of finite classical groups

Tim C Burness, Robert M Guralnick, Jan Saxl

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

13 Citations (Scopus)
20 Downloads (Pure)


Let G be a permutation group on a set X. A subset B of X is a base for G if the pointwise stabilizer of B in G is trivial; the base size of G is the minimal cardinality of a base for G, denoted by b(G). In this paper we calculate the base size of every primitive almost simple classical group with point stabilizer in Aschbacher’s collection S of irreducibly embedded almost simple subgroups. In this situation we also establish strong asymptotic results on the probability that randomly chosen subsets of X form a base for G. Indeed, with some specific exceptions, we show that almost all pairs of points in X are bases.
Original languageEnglish
Pages (from-to)711-756
Number of pages46
JournalIsrael Journal of Mathematics
Publication statusPublished - 2014


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