A 5-local identification of the Monster.
type: Item
instance of: scholarly article
title: A 5-local identification of the Monster.
zbMATH Open document ID: 1071.20022
published in: Archiv der Mathematik
publication date: 2005-02-25T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.nmj/1124217074
review text: This paper provides a characterization of the Monster sporadic simple group in terms of its 5-local structure. Under the general hypothesis that every composition factor of every local subgroup of \(G\) is a known simple group, it is shown that if \(G\) is a finite group with a Sylow 5-subgroup having centre \(Z\) of order 5, and \(N_G(Z)\) is of shape \(5^{1+6}4J_2.2\), then subject to the non-triviality conditions that \(4J_2.2\) acts faithfully on \(Q\cong 5^{1+6}\) and that \(Q\) contains more than one \(G\)-conjugate of \(Z\), in fact \(G\) is the Monster. The context of this work is the classification of groups of `local characteristic \(p\)', where many of the ideas from the Classification of Finite Simple Groups are generalized from the prime 2 to arbitrary primes \(p\).
Mathematics Subject Classification ID: 20D08
Mathematics Subject Classification ID: 20D20
zbMATH DE Number: 2138532
zbMATH Keywords: Monster
zbMATH Keywords: sporadic groups
zbMATH Keywords: amalgams
zbMATH Keywords: local subgroups
author: Chris Parker
author: Corinna Wiedorn
reviewed by: Robert A. Wilson
MaRDI profile type: Publication
OpenAlex ID: W2917238485
DOI: 10.1007/S00013-004-1171-3
description: scientific article; zbMATH DE number 2138532