Abstract
For each partition Îť of n , let L Îť = L Îť ( p ) be the lattice of subgroups of a finite Abelian p -group of type Îť. We study a topological condition necessary for the existence of an order-preserving injection of L Îź into L Îť . Our main result shows this topological condition is equivalent to the simple requirement that Îź dominates Îť. We employ results obtained by Lascoux and SchĂźtzenberger in the theory of HallâLittlewood symmetric functions.
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