Constructions of Fischer's Baby Monster over fields of characteristic not \(2\)
type: Item
instance of: scholarly article
title: Constructions of Fischer's Baby Monster over fields of characteristic not \(2\)
zbMATH Open document ID: 0963.20006
author: Richard A. Parker
author: Robert A. Wilson
published in: Journal of Algebra
publication date: 2001-03-15T00:00:00Z
review text: The authors give a description of the computer construction of \(4371\)-dimensional representations over the fields \(\text{GF}(3)\) and \(\text{GF}(5)\) for Fischer's Baby Monster group \(B\). As an application they also obtain \(3\)-modular and \(5\)-modular representations for the sporadic simple Thompson group which in turn will assist in determining the corresponding Brauer character tables. The strategy employed is to construct the appropriate representation for a maximal \(2\)-local subgroup \(H\cong 2^{1+22}.Co_2\) first, then restrict to a subgroup \(D\cong 2^{2+10+20}.M_{22}\) of \(H\), and finally adjoin an outer automorphism \(\alpha\) of order \(3\) to \(D\) in order to get the relevant representation for \(M=D:\langle\alpha\rangle\). In this way, \(B\) is constructed as a finite completion of the free amalgamated product \(H*_DM\) of \(H\) and \(M\) over \(D\).
reviewed by: Wolfgang Lempken
Mathematics Subject Classification ID: 20C34
Mathematics Subject Classification ID: 20C40
Mathematics Subject Classification ID: 20D08
Mathematics Subject Classification ID: 20C20
zbMATH DE Number: 1496006
zbMATH Keywords: modular representations
zbMATH Keywords: sporadic groups
zbMATH Keywords: Fischer's Baby Monster
zbMATH Keywords: Brauer character tables
describes a project that uses: MeatAxe
MaRDI profile type: Publication
full work available at URL: jabr.2000.8301
OpenAlex ID: W2071241118
cites work: Q3684278
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cites work: Computer construction of the Monster
cites work: Q3218280
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cites work: Standard generators for sporadic simple groups
DOI: 10.1006/JABR.2000.8301
description: scientific article; zbMATH DE number 1496006