Normalized matching property of the subgroup lattice of an abelian p-group

AbstractLet L(kn)(p) denote the subgroup lattice of the abelian p-group(Z/pkZ)×⋯×(Z/pkZ)(ntimes).In a previous paper (Ann. of Combin. 2 (1998) 85), we proved that L(kn)(p) has the Sperner property. In this paper, we prove that for any positive integers n and k, there is a positive integer N(n,k) such that L(kn)(p) has the normalized matching property when p>N(n,k). As a consequence, L(kn)(p) has the strong Sperner property, LYM property and it is a symmetric chain order when p is sufficiently large