Independent generating sets and geometries for symmetric groups

Julius Whiston showed that the size of an independent generating set in the symmetric group Sn is at most n−1. We determine all sets meeting this bound. We also give some general remarks on the maximum size of an independent generating set of a group and its relationship to coset geometries for the group. In particular, we determine all coset geometries of maximum rank for the symmetric group Sn for n>6.