Generating sets for subgroups of symmetric groups

This article provides summary information on generating sets for subgroups of the symmetric group of degree $$n$$. The basic facts and computational procedures are as follows:


 * Subgroup rank of symmetric group is about half the degree: This states that the subgroup rank is $$n/2$$ for even $$n$$ and $$(n-1)/2$$ for odd $$n$$, except $$n = 3$$ where it equals 2.
 * Jerrum's filter is a computational procedure for taking any generating set for a subgroup of the symmetric group of degree $$n$$ and obtaining from that a generating set of size at most $$n - 1$$.
 * Sims filter is a computational procedure for taking any generating set for a subgroup of the symmetric group of degree $$n$$ and obtaining from it a subgroup of size at most $$n(n-1)/2$$.
 * Symmetric group on a finite set is 2-generated, alternating group on a finite set is 2-generated, and Dixon's theorem.