Strong Sperner property of the subgroup lattice of an Abelian \(p\)-group
type: Item
instance of: scholarly article
title: Strong Sperner property of the subgroup lattice of an Abelian \(p\)-group
zbMATH Open document ID: 0970.06005
DOI: 10.1007/BF02878435
author: Jun Wang
author: Yi Wang
published in: Science in China. Series A
publication date: 2000-12-12T00:00:00Z
review text: Let \(P\) be a graded poset. If for all \(m\), the cardinality of a subset of \(P\) (which does not contain a chain of length \(m+1\)) does not exceed the cardinality of the union of the \(m\) largest ranks of \(P\) then we say \(P\) is strongly Sperner. In this paper the authors use some technical lemmas to prove that for given \(n\) and \(k\) and a large enough prime, \(p\), the subgroup lattice \(L_{(k^1)}(p)\) of the Abelian \(p\)-group \((\mathbb{Z}/p^k\mathbb{Z})^n\) is strongly Sperner.
Mathematics Subject Classification ID: 06A07
Mathematics Subject Classification ID: 05D05
Mathematics Subject Classification ID: 20D30
zbMATH DE Number: 1542543
zbMATH Keywords: strong Sperner property
zbMATH Keywords: graded poset
zbMATH Keywords: subgroup lattice
zbMATH Keywords: Abelian \(p\)-group
reviewed by: Stephanie van Willigenburg
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02878435
OpenAlex ID: W1573176904
description: scientific article; zbMATH DE number 1542543