  Let $G =<S>$ be a solvable permutation group of the symmetric group $S_n$
given as input by the generating set $S$. We give a deterministic
polynomial-time algorithm that computes an \emph{expanding generating set} of
size $\tilde{O}(n^2)$ for $G$. More precisely, the algorithm computes a subset
$T\subset G$ of size $\tilde{O}(n^2)(1/\lambda)^{O(1)}$ such that the
undirected Cayley graph $Cay(G,T)$ is a $\lambda$-spectral expander (the
$\tilde{O}$ notation suppresses $\log ^{O(1)}n$ factors). As a byproduct of our
proof, we get a new explicit construction of $\varepsilon$-bias spaces of size
$\tilde{O}(n\poly(\log d))(\frac{1}{\varepsilon})^{O(1)}$ for the groups
$\Z_d^n$. The earlier known size bound was $O((d+n/\varepsilon^2))^{11/2}$
given by \cite{AMN98}.
