Chamber Graphs of Minimal Parabolic Geometries of Type M_24

Carr, Emily and Rowley, Peter (2018) Chamber Graphs of Minimal Parabolic Geometries of Type M_24. [MIMS Preprint]

Text ChamberGraphsParabolicSystemsof TypeM_24.pdf Download (272kB)

Abstract

This paper investigates the structure of the chamber graph associated with the minimal parabolic geometries of rank 3 for the groups M24, the Mathieu group of degree 24, He, Held's simple group, and 37_Sp6(2), a non-split extension of an elementary abelian 3-group with Sp6(2). These three minmal parabolic geometries all have the same diagram. Executable �les containing data describing the disc structure of a �xed chamber of these graphs accompany this paper. Those chambers at maximal distance from a given chamber are studied, as are the maximal opposite sets. Also the geodesic closure of opposite chambers are described for each of these three geometries.

Item Type:	MIMS Preprint
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations
Depositing User:	Professor Peter Rowley
Date Deposited:	06 Aug 2018 04:28
Last Modified:	06 Aug 2018 04:28
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/2647

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