Irredundant bases for soluble groups

Let be a finite set and be a subgroup of . An irredundant base for is a sequence of points of yielding a strictly descending chain of pointwise stabilisers, terminating with the trivial group. Suppose that is primitive and soluble. We determine asymptotically tight bounds for the maximum length of an irredundant base for . Moreover, we disprove a conjecture of Seress on the maximum length of an irredundant base constructed by the natural greedy algorithm, and prove Cameron's Greedy Conjecture for odd.