Regular Article
Flat Lax and Weak Lax Embeddings of Finite Generalized Hexagons

https://doi.org/10.1006/eujc.1998.0240Get rights and content
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Abstract

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

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The second author is a Research Director of the Fund for Scientific Research, Flanders, Belgium.