Abstract
Let\(L_{\left( {k^n } \right)}\)(p) denote the subgroup lattice of the abelianp-group
. It is conjectured that the lattice has the Sperner property. Whenk=1, the conjecture is true since it is isomorphic to the subspace lattice, and Stanley has confirmed it fork=2. In this paper, we prove that the conjecture is generally true.
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Wang, J. Proof of a conjecture on the Sperner property of the subgroup lattice of an abelianp-group. Annals of Combinatorics 2, 85–101 (1998). https://doi.org/10.1007/BF01626030
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DOI: https://doi.org/10.1007/BF01626030