On the order of a group of even order.
type: Item
instance of: scholarly article
title: On the order of a group of even order.
zbMATH Open document ID: 1119.20017
author: Koichiro Harada
author: Masahiko Miyamoto
published in: Journal of Algebra
publication date: 2007-04-16T00:00:00Z
review text: Let \(G\) be a group of even order with a unique conjugacy class of involutions. In the paper under review the authors provide an upper bound for the order of \(G\) in terms of the centralizer \(H=C_G(t)\) of an involution \(t\) in \(G\). As an application the authors provide examples of sporadic simple groups, the groups \(Ly\) and \(Th\), whose orders could be found using the upper bound obtained in this paper.
Mathematics Subject Classification ID: 20D08
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 5143564
zbMATH Keywords: finite groups
zbMATH Keywords: sporadic simple groups
zbMATH Keywords: groups of even order
zbMATH Keywords: centralizers of involutions
zbMATH Keywords: order formulae
reviewed by: M. R. Darafsheh
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2006.09.028
OpenAlex ID: W2051004229
Wikidata QID: Q112881500
cites work: The classification of the finite simple groups
cites work: On groups of even order
cites work: Evidence for a new finite simple group
cites work: Q5639819
cites work: On Thompson's simple group
cites work: On Finite Groups with Cyclic Sylow Subgroups for all Odd Primes
DOI: 10.1016/J.JALGEBRA.2006.09.028
description: scientific article; zbMATH DE number 5143564