Covering numbers for Chevalley groups
type: Item
instance of: scholarly article
title: Covering numbers for Chevalley groups
zbMATH Open document ID: 0941.20050
DOI: 10.1007/BF02810691
author: Erich W. Ellers
author: N. L. Gordeev
author: Marcel Herzog
published in: Israel Journal of Mathematics
publication date: 2000-05-16T00:00:00Z
review text: Let \(G\) be a group. For a subset \(X\) of \(G\), let \(X^n\) denote the set of elements \(x_1\cdots x_n\), where \(x_i\in X\). If \(\mathfrak A\) is a set of subsets of \(G\), it is interesting to consider the problem to determine the smallest integer \(n\) such that \(X^n=G\) for all \(X\in{\mathfrak A}\). This is called the covering number, denoted by \(\text{cn}(G)\). The authors prove that, if \(G\) is a quasisimple Chevalley group with rank \(r\) and \(\mathfrak A\) is the set of non-central conjugacy classes, then there is a constant \(d\) such that \(\text{cn}(G)\leq dr\).
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 20H20
Mathematics Subject Classification ID: 20E45
Mathematics Subject Classification ID: 20F05
zbMATH DE Number: 1356483
zbMATH Keywords: Chevalley groups
zbMATH Keywords: quasisimple groups
zbMATH Keywords: covering numbers
zbMATH Keywords: conjugacy classes
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1356483