A note on two-generator groups
type: Item
instance of: scholarly article
title: A note on two-generator groups
zbMATH Open document ID: 0688.20012
DOI: 10.1216/RMJ-1987-17-4-887
author: Martin J. Evans
published in: Rocky Mountain Journal of Mathematics
publication date: 1987-01-01T00:00:00Z
review text: The author studies the property (*): For any \(g\in G\) there is some \(h\in G\) such that \(<g,h>=G\) and either g or h is an involution. He shows that the Suzuki groups Sz(q) have property (*). Furthermore he shows that a simple Chevalley group over a field of odd characteristic having property (*) has to be isomorphic to PSL(2,q), for some odd q. This is done by using the known structure of the subgroups of Chevalley groups generated by two root elements, which usually are not the whole group.
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20D05
Mathematics Subject Classification ID: 20G40
Mathematics Subject Classification ID: 20E32
zbMATH DE Number: 4127489
zbMATH Keywords: involution
zbMATH Keywords: Suzuki groups
zbMATH Keywords: simple Chevalley group
zbMATH Keywords: root elements
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4127489