Near-Optimal Expanding Generator Sets for Solvable Permutation Groups

Let G = < S > be a solvable subgroup of the symmetric group Sn given as input by the generator set S. We give a deterministic polynomial-time algorithm that computes an expanding generator set of size (O) over tilde (n(2)) for G. As a byproduct of our proof, we obtain a new explicit construction of epsilon-bias spaces of size (O) over tilde (n poly(log d))(1/epsilon)(O(1)) for the groups Z(d)(n).