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

Authors:
Jun Wang
Affiliations:
Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China
Venue:
Discrete Mathematics - Kleitman and combinatorics: a celebration
Year:
2002

Citing 6
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Abstract

Let L(kn)(p) denote the subgroup lattice of the abelian p-group (Z/pkZ) × ... × (Z/pkZ) (n times). 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.