Near-optimal expanding generator sets for solvable permutation groups

Abstract

Let G = 〈S〉 be a solvable subgroup of the symmetric group S n given as input by the generator set S. We give a deterministic polynomial-time algorithm that computes an expanding generator set of size Õ(n 2) for G. As a byproduct of our proof, we obtain a new explicit construction of ε-bias spaces of size Õ for the groups . © 2012 Springer-Verlag.