Products of conjugacy classes in Chevalley groups. II: Covering and generation
type: Item
instance of: scholarly article
title: Products of conjugacy classes in Chevalley groups. II: Covering and generation
zbMATH Open document ID: 1007.20042
DOI: 10.1007/BF02764078
author: N. L. Gordeev
author: Jan Saxl
published in: Israel Journal of Mathematics
publication date: 2003-01-01T00:00:00Z
review text: [For part I see the preceding review Zbl 1007.20041.] Let \(G\) be a simple algebraic group over an algebraically closed field \(K\). Let \(C\) be a conjugacy class of \(G\). Define the covering number \(\text{cn}(G)\) and the generating number \(\overline{\text{gen}}(G)\) as follows: \[ \text{cn}(G)=\min\{m\mid C^m=G\}, \] \[ \overline{\text{gen}}(G)=\min\{m\mid\text{there are }g_i\in C\text{ such that }\overline{\langle g_1,\dots,g_m\rangle}=G\}. \] The authors investigate the relationship between generating numbers and covering numbers. They obtain results such as \[ {1\over 2}\text{cn}(G)\leq\overline{\text{gen}}(G)\leq\text{cn}(G)+1. \]
reviewed by: Erich W. Ellers
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20E45
zbMATH DE Number: 1799794
zbMATH Keywords: covering numbers
zbMATH Keywords: generating numbers
zbMATH Keywords: conjugacy classes
zbMATH Keywords: Chevalley groups
MaRDI profile type: Publication
cites work: Q3999894
cites work: Q5580319
cites work: Q3996420
cites work: Products of conjugacy classes in algebraic groups. I
cites work: Products of conjugacy classes in Chevalley groups. I: Extended covering numbers
cites work: Q4217761
cites work: Probabilistic generation of finite simple groups
cites work: Diameters of finite simple groups: sharp bounds and applications
cites work: Lectures on Chevalley Groups
full work available at URL: https://doi.org/10.1007/bf02764078
OpenAlex ID: W2033339399
description: scientific article; zbMATH DE number 1799794