For each partition λ of n, let LÅλ=LÅλ(p) be the lattice of subgroups of a finite Abelian p-group of type λ. The paper studies a topological condition necessary for the existence of an order-preserving injection of LÅμ into LÅλ. The present main result shows this topological condition is equivalent to the simple requirement that μ dominates λ. It employs results obtained by Lascoux and Schützenberger in the theory of Hall-Littlewood symmetric functions.
