Abstract
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 language | English |
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Pages (from-to) | 711-756 |
Number of pages | 46 |
Journal | Israel Journal of Mathematics |
Volume | 199 |
DOIs | |
Publication status | Published - 2014 |