Generation of finite almost simple groups by conjugates.
type: Item
instance of: scholarly article
title: Generation of finite almost simple groups by conjugates.
zbMATH Open document ID: 1037.20016
DOI: 10.1016/S0021-8693(03)00182-0
author: Jan Saxl
author: Robert Guralnick
published in: Journal of Algebra
publication date: 2003-12-03T00:00:00Z
review text: Let \(G\) be a finite almost simple group and \(L=F^*(G)\). For \(x\in G\), let \(\alpha(x)\) be the minimal number of \(L\)-conjugates of \(x\) which generate the group \(\langle L,x\rangle\). The authors obtain some upper bounds on \(\alpha(x)\). For example, if \(L\) is a simple classical group of dimension at least 5 and \(x\in\Aut(L)\) then \(\alpha(x)\leq n\), unless \(L=\text{Sp}_n(q)\) with \(q\) even, \(x\) is a transvection and \(\alpha(x)=n+1\) (Theorem 4.2).
reviewed by: V. D. Mazurov
Mathematics Subject Classification ID: 20D06
Mathematics Subject Classification ID: 20F05
zbMATH DE Number: 2012748
zbMATH Keywords: classical groups
zbMATH Keywords: exceptional groups
zbMATH Keywords: groups of Lie type
zbMATH Keywords: finite almost simple groups
zbMATH Keywords: Fitting subgroup
zbMATH Keywords: numbers of generators
MaRDI profile type: Publication
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full work available at URL: s0021-8693(03)00182-0

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