On point orbits of the \(Co_2\)-minimal parabolic geometry.
type: Item
instance of: scholarly article
title: On point orbits of the \(Co_2\)-minimal parabolic geometry.
zbMATH Open document ID: 1072.51015
author: Louise Walker
author: Peter J. Rowley
published in: Journal of Combinatorial Theory. Series A
publication date: 2004-10-01T00:00:00Z
review text: In [Eur. J. Comb. 5, 59--91 (1984; Zbl 0574.20012)] \textit{M. Ronan} and the reviewer introduced a rank three minimal parabolic geometry for \(Co_2\). In this paper the authors investigate the point-line collinearity graph of this geometry. They gather a lot of results, among them the \(H\)-orbits of subgroups of \(Co_2\) isomorphic to \((2^{1+6}\times 2^4)A_8\), \(2^{1+8}Sp_6(2)\), \(2^{10}2^4S_6\), \(2^{1+8}U_4(2)2\), \(U_6(2)2\) and \(HS2\). This all will be done by embedding the graph into the Leech-lattice and then studying this lattice. The results then will be used in [J. Comb. Theory, Ser A 107, 181--213, 215--261 (2004; Zbl 1077.20029)], where the authors determine the point-line collinearity graph for the Baby Monster geometry.
reviewed by: Gernot Stroth
Mathematics Subject Classification ID: 51E24
Mathematics Subject Classification ID: 20D08
zbMATH DE Number: 2105514
zbMATH Keywords: point-line collinearity graph
MaRDI profile type: Publication
full work available at URL: j.jcta.2004.04.008
OpenAlex ID: W1974571809
cites work: Q3684278
cites work: A new combinatorial approach to M24
cites work: Minimal parabolic geometries for the sporadic groups
cites work: Q4839312
cites work: A 11,707,448,673,375 vertex graph related to the Baby Monster. I, II.
DOI: 10.1016/J.JCTA.2004.04.008
description: scientific article; zbMATH DE number 2105514