Symmetric Chain Decompositions of Quotients of Chain Products by Wreath Products

Subgroups of the symmetric group Sn act on powers of chains C n by permuting coordinates, and induce automorphisms of the ordered sets C. The quotients defined are candidates for symmetric chain decompositions. We establish this for some families of groups in order to enlarge the collection of subgroups G of the symmetric group Sn for which the quotient Bn/G obtained from the G-orbits on the Boolean lattice Bn is a symmetric chain order. The methods are also used to provide an elementary proof that quotients of powers of SCOs by cyclic groups are SCOs.