Abstract
Let G be a permutation group on a finite set Ω of size n. A subset of Ω is said to be a base for G if its pointwise stabilizer in G is trivial. The minimal size of a base for G is denoted by b(G). Bases have been studied since the early years of permutation group theory, particularly in connection with orders of primitive groups and, more recently, with computational group theory. In this paper we survey some of the recent developments in this area, with particular emphasis on some well known conjectures of Babai, Cameron and Pyber.
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