Independent generating sets and geometries for symmetric groups

Julius Whiston showed that the size of an independent generating set in the symmetric group S(n) 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 S(n) for n > 6. (C) 2002 Elsevier Science (USA). All rights reserved.