Two remarks on generalized hexagons
type: Item
instance of: scholarly article
title: Two remarks on generalized hexagons
zbMATH Open document ID: 0969.51006
DOI: 10.1007/BF01220303
author: Eline Govaert
author: Hendrik Van Maldeghem
published in: Journal of Geometry
publication date: 2001-10-02T00:00:00Z
review text: The only known finite generalized hexagons were presented by \textit{J. Tits} in his famous triality paper [Publ. Math. Inst. Hautes Étud. Sci. 2, 13--60 (1959; Zbl 0088.37204)] and belong to two infinite families associated with finite simple groups. These are the only finite Moufang hexagons (i.e., admitting collineation groups with certain specified transitivity properties). The hexagons related to the groups \(G_2(q)\) are called the split Cayley hexagons and denoted \(H(q)\). In the paper under review the authors give some technical but quite interesting combinatorial characterizations of the known hexagons, and especially of the \(H(q)\) with \(q\) even. The definitions seem a bit involved for a review, but these results build on the work of \textit{J. van Bon}, \textit{H. Cuypers} and \textit{H. Van Maldeghem} [Forum Math. 8, No. 3, 343--362 (1994; Zbl 0854.51004)] and on the much earlier work of \textit{M. A. Ronan} [Geom. Dedicata 11, 61--67 (1981; Zbl 0485.51014)].
reviewed by: Stanley E. Payne
Mathematics Subject Classification ID: 51E12
zbMATH DE Number: 1443428
zbMATH Keywords: split Cayley hexagons
zbMATH Keywords: finite Moufang hexagons
MaRDI profile type: Publication
cites work: A combinatorial characterization of the dual Moufang hexagons
cites work: Sur la trialité et certains groupes qui s'en déduisent
cites work: Q4217275
full work available at URL: https://doi.org/10.1007/bf01220303
OpenAlex ID: W2047820446
description: scientific article; zbMATH DE number 1443428