Irredundant bases for the symmetric group

Abstract

An irredundant base of a group acting faithfully on a finite set Γ is a sequence of points in Γ that produces a strictly descending chain of pointwise stabiliser sub-groups in ,terminating at the trivial subgroup. Suppose that is S or A acting primitively on Γ, and that the point stabiliser is primitive in its natural action onpoints. We prove that the maximum size of an irredundant base of is (√),and in most cases ((log)2). We also show that these bounds are best possible.