Low dimensional models of the finite split Cayley hexagon

We provide a model of the split Cayley hexagon arising from the Hermitian surface $\mathsf{H}(3,q^2)$, thereby yielding a geometric construction of the Dickson group $G_2(q)$ starting with the unitary group $\mathsf{SU}_3(q)$

Some Remarks on Steiner Systems

The main purpose of this paper is to introduce Steiner systems obtained from the finite classical generalized hexagons of order q. We show that we can take the blocks of the Steiner systems amongst the lines and the traces of the hexagon, and we prove some facts about the automorphism groups. Also, we make a remark concerning the geometric construction of a known class (KW) of Steiner systems and we deduce some properties of the automorphism group

Flat lax and weak lax embeddings of finite generalized hexagons

AbstractIn 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