Embeddings of an \(M_{12}\) geometry: Some simple combinatorial descriptions
type: Item
instance of: scholarly article
title: Embeddings of an \(M_{12}\) geometry: Some simple combinatorial descriptions
zbMATH Open document ID: 0646.20017
DOI: 10.1016/S0195-6698(88)80045-3
author: Sarah Rees
published in: European Journal of Combinatorics
publication date: 1988-01-01T00:00:00Z
review text: The author describes the 2-local geometry for \(M_{12}\) as a set of 1- spaces and 2-spaces of a 10-dimensional or a 44-dimensional module for \(M_{12}\) over GF(2). The key idea is to describe these modules as sets of certain graphs for the group \(M_{12}\). This graph method works very well and so one can describe the embedding of the geometry into the corresponding module very nicely. The author suggests to describe geometries for other groups by the same method.
Mathematics Subject Classification ID: 20D08
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 51E30
Mathematics Subject Classification ID: 20B25
zbMATH DE Number: 4053893
zbMATH Keywords: Mathieu groups
zbMATH Keywords: 2-local geometry for \(M_{12}\)
zbMATH Keywords: graphs
zbMATH Keywords: embedding
reviewed by: Gernot Stroth
MaRDI profile type: Publication
cites work: Q3356325
cites work: Q3668381
cites work: On the foundations of polar geometry
cites work: Q3739329
cites work: Automorphisms of trivalent graphs
cites work: The modular characters of the Mathieu groups
cites work: Sheaves on buildings and modular representations of Chevalley groups
cites work: Minimal parabolic geometries for the sporadic groups
cites work: Q3317118
full work available at URL: s0195-6698(88)80045-3
OpenAlex ID: W2092651087
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description: scientific article; zbMATH DE number 4053893