Flat Lax and Weak Lax Embeddings of Finite Generalized Hexagons

✍ Scribed by J.A. Thas; H. Van Maldeghem

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 309 KB
• Volume: 19
• Category: Article
• ISSN: 0195-6698
• DOI: 10.1006/eujc.1998.0240

✦ Synopsis

In this paper we study laxly embedded generalized hexagons in finite projective spaces (a generalized hexagon is laxly embedded in PG(d, q) if it is a spanning subgeometry of the natural point-line geometry associated to PG(d, q)), satisfying the following additional assumption: for any point x of the hexagon, the set of points collinear in the hexagon with x is contained in some plane of PG(d, q). In particular, we show that d ≤ 7, and if d = 7, we completely classify all such embeddings. A classification is also carried out for d = 5, 6 under some additional hypotheses. Finally, laxly embedded generalized hexagons satisfying other additional assumptions are considered, and classifications are also obtained.