Ree geometries
Group Theory
2009-09-18 v1 Combinatorics
Abstract
We introduce a rank 3 geometry for any Ree group over a not necessarily perfect field and show that its full collineation group is the automorphism group of the corresponding Ree group. A similar result holds for two rank 2 geometries obtained as a truncation of this rank 3 geometry. As an application, we show that a polarity in any Moufang generalized hexagon is unambiguously determined by its set of absolute points, or equivalently, its set of absolute lines.
Cite
@article{arxiv.0909.3211,
title = {Ree geometries},
author = {Fabienne Haot and Koen Struyve and Hendrik Van Maldeghem},
journal= {arXiv preprint arXiv:0909.3211},
year = {2009}
}