Simple connectedness of the 3-local geometry of the Monster
type: Item
instance of: scholarly article
title: Simple connectedness of the 3-local geometry of the Monster
zbMATH Open document ID: 0888.51011
author: U. Meierfrankenfeld
author: Alexander A. Ivanov
published in: Journal of Algebra
publication date: 1998-05-13T00:00:00Z
review text: The Monster group \(M\) gives rise to a 3-local geometry \(\mathcal M\) which is determined in terms of a certain subgroup of \(M\) extending the simple orthogonal group \(\Omega_8^-(3)\). The main result of the paper is that \(\mathcal M\) is simply connected, which is equivalent to the fact that \(M\) is the universal completion of the amalgam of maximal parabolic subgroups corresponding to the flag-transitive action of \(M\) on \(\mathcal M\). In order to prove this theorem, the authors make use of the simple connectedness results for the 2-local geometry of \(M\) and for a subgeometry in \(\mathcal M\) which is the 3-local geometry of the Fischer group \(M(24)\). The result makes unnecessary the refereeing to the classification of finite simple groups in a recent \(Z_3\)-orbifold construction of the Moonshine module.
Mathematics Subject Classification ID: 51E24
Mathematics Subject Classification ID: 20D08
zbMATH DE Number: 1066129
zbMATH Keywords: Monster group
zbMATH Keywords: diagram geometry
zbMATH Keywords: sporadic simple groups
zbMATH Keywords: local geometries
zbMATH Keywords: strongly regular graph
reviewed by: Dirk Hachenberger
MaRDI profile type: Publication
full work available at URL: jabr.1997.7026
OpenAlex ID: W1979127447
cites work: Q4295765
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DOI: 10.1006/JABR.1997.7026
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description: scientific article; zbMATH DE number 1066129