Strong Sperner property of the subgroup lattice of an Abelian p-group

摘要

Let n and k be arbitrary positive integers, p a prime number and L(kn)(p) the subgroup lattice of the Abelian p-group ( /pk )n. Then there is a positive integer N( n, k) such that when p N( n, k), L(kn)(p) has the strong Sperner property.