The largest lengths of conjugacy classes and the Sylow subgroups of finite groups.
type: Item
instance of: scholarly article
title: The largest lengths of conjugacy classes and the Sylow subgroups of finite groups.
zbMATH Open document ID: 1098.20020
author: Liguo He
author: Shi Wujie
published in: Archiv der Mathematik
publication date: 2006-03-21T00:00:00Z
review text: From the authors' summary: Let \(G\) be a finite nonabelian group, \(P\in\text{Syl}_p(G)\), and \(\text{bcl}(G)\) the largest length of conjugacy classes of \(G\). In this short paper, we prove that \(\sqrt{|P/O_p(G)|}<\text{bcl}(G)\) in general and \(|P/O_p(G)|<\text{bcl}(G)\) in the case where \(P\) is Abelian.
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20E45
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D06
zbMATH DE Number: 5013985
zbMATH Keywords: sporadic simple groups
zbMATH Keywords: groups of Lie type
zbMATH Keywords: lengths of conjugacy classes
zbMATH Keywords: Sylow subgroups
zbMATH Keywords: finite groups
MaRDI profile type: Publication
full work available at URL: s00013-005-1408-9
OpenAlex ID: W2088114124
DOI: 10.1007/S00013-005-1408-9
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description: scientific article; zbMATH DE number 5013985