Minimal covers of \(S_ n\) by abelian subgroups and maximal subsets of pairwise noncommuting elements. II
type: Item
instance of: scholarly article
title: Minimal covers of \(S_ n\) by abelian subgroups and maximal subsets of pairwise noncommuting elements. II
zbMATH Open document ID: 0715.20004
DOI: 10.1016/0097-3165(91)90037-H
author: D. Kharzeev
published in: Journal of Combinatorial Theory. Series A
publication date: 1991-01-01T00:00:00Z
review text: The author follows up the investigations in his earlier paper [Part I, ibid. 49, No.2, 294-307 (1988; Zbl 0666.20012)] with new conclusions about the minimum cardinality \(\beta_ n\) of a cover of the symmetric group \(S_ n\) by abelian subgroups, and the maximum cardinality \(\alpha_ n\) of a set of pairwise non-commuting elements of \(S_ n\). He now shows that \(\alpha_ n\neq \beta_ n\) for \(n=8\), 13 and all \(n\geq 15\), and that the ratio \(\beta_ n/\alpha_ n\) has no limit and takes infinitely many values arbitrary close to 1.
Mathematics Subject Classification ID: 20B35
Mathematics Subject Classification ID: 20D30
Mathematics Subject Classification ID: 11N45
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 4177358
zbMATH Keywords: cover
zbMATH Keywords: symmetric group
zbMATH Keywords: abelian subgroups
zbMATH Keywords: non-commuting elements
reviewed by: John Knopfmacher
MaRDI profile type: Publication
cites work: Minimal covers of \(S_ n\) by Abelian subgroups and maximal subsets of pairwise noncommuting elements
cites work: Q5331572
full work available at URL: 0097-3165(91)90037-h
OpenAlex ID: W4255567901
description: scientific article; zbMATH DE number 4177358