Baer-Suzuki theorem for the solvable radical of a finite group.
type: Item
instance of: scholarly article
title: Baer-Suzuki theorem for the solvable radical of a finite group.
zbMATH Open document ID: 1167.20012
author: J. Martínez
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2009-04-02T00:00:00Z
review text: An outline of proof (using the CFSG) is given to the following analogue of a theorem of Baer-Suzuki: Theorem 1.4. Let \(G\) be a finite group. An element \(g\) of prime order \(q>3\) belongs to the solvable radical \(S(G)\) of \(G\) if and only if for any \(x\in G\) the subgroup \(\langle g,x^{-1}gx\rangle\) is solvable. As a corollary, it follows that a finite group \(G\) is solvable if and only if in each conjugacy class of \(G\) every two elements generate a solvable subgroup.
reviewed by: Marian Deaconescu
Mathematics Subject Classification ID: 20D25
Mathematics Subject Classification ID: 20D05
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20E45
Mathematics Subject Classification ID: 20D10
zbMATH DE Number: 5539118
zbMATH Keywords: solvable radical
zbMATH Keywords: finite groups
zbMATH Keywords: conjugacy classes
zbMATH Keywords: solvable groups
zbMATH Keywords: Baer-Suzuki theorem
MaRDI profile type: Publication
full work available at URL: j.crma.2009.01.004
OpenAlex ID: W2152546755
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DOI: 10.1016/J.CRMA.2009.01.004
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description: scientific article; zbMATH DE number 5539118