Annals of Combinatorics 2 (1998) 85-101

Proof of a Conjecture on the Sperner Property of the Subgroup Lattice of an Abelian p-Group

Jun Wang

Institute of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China

Received March 15, 1997

AMS Subject Classification: 05A05, 05D05,06A07

Abstract. Let L(kn)(p) denote the subgroup lattice of the abelian p-group

(Z/pkZ) × ··· × (Z/pkZ) (n times).
It is conjectured that the lattice has the Sperner property. When k=1, the conjecture is true since it is isomorphic to the subspace lattice, and Stanley has confirmed it for k=2. In this paper, we prove that the conjecture is generally true.

Keywords: Sperner property, poset, subgroup lattice


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