Vol. 18, No. 1, 2020

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Chamber graphs of minimal parabolic sporadic geometries

Veronica Kelsey and Peter Rowley

Vol. 18 (2020), No. 1, 25–37
Abstract

We explore the minimal characteristic two parabolic geometries for the finite sporadic simple groups, as introduced by Ronan and Stroth. The chamber graphs of the geometries are studied, with the aid of Magma, focusing on their disc structure and geodesic closures. For the larger sporadic geometries which are beyond computational reach we give bounds on the diameter of their chamber graphs.

Keywords
chamber graph, geometries, sporadic simple groups
Mathematical Subject Classification 2010
Primary: 51E24
Secondary: 05B25
Milestones
Received: 25 September 2019
Revised: 2 March 2020
Accepted: 17 March 2020
Published: 15 October 2020
Authors
Veronica Kelsey
School of Mathematics and Statistics
University of St Andrews
St Andrews
KY16 9SS
United Kingdom
Peter Rowley
Department of Mathematics
Manchester University
Manchester
M13 6PL
United Kingdom