A note on near hexagons with lines of size 3

We classify all finite near hexagons which satisfy the following properties for a certain t(2) is an element of {1, 2, 4}: (i) every line is incident with precisely three points; (ii) for every point x, there exists a point y at distance 3 from x; (iii) every two points at distance 2 from each other have either 1 or t(2) + 1 common neighbours; (iv) every quad is big. As a corollary, we obtain a classification of all finite near hexagons satisfying (i), (ii) and (iii) with t(2) equal to 4.

http://ift.tt/2sw78YN