  R. Canfield has conjectured that for all subgroups G of the automorphism
group of the Boolean lattice B(n) (which can be regarded as the symmetric group
S(n)) the quotient order B(n)/G is a symmetric chain order. We provide a
straightforward proof of a generalization of a result of K. K. Jordan: namely,
B(n)/G is an SCO whenever G is generated by powers of disjoint cycles. The
symmetric chain decompositions of Greene and Kleitman provide the basis for
partitions of these quotients.
