New constructions of two slim dense near hexagons
نویسنده
چکیده
We provide a geometrical construction of the unique slim dense near hexagon with parameters (s, t, t2) = (2, 5, {1, 2}). Using this construction, we construct the rank 3 symplectic dual polar space DSp(6, 2) which is the unique slim dense near hexagon with parameters (s, t, t2) = (2, 6, 2). Both near hexagons are constructed from two copies of the unique generalized quadrangle with parameters (2,2). Mathematics Subject Classification (2000). 51E12
منابع مشابه
Non-abelian representations of the slim dense near hexagons on 81 and 243 points
We prove that the near hexagon Q(5,2)× L3 has a non-abelian representation in the extra-special 2-group 21+12 + and that the near hexagon Q(5,2)⊗Q(5,2) has a non-abelian representation in the extra-special 2-group 21+18 − . The description of the non-abelian representation of Q(5,2)⊗Q(5,2) makes use of a new combinatorial construction of this near hexagon.
متن کاملOn Near Hexagons and Spreads of Generalized Quadrangles
The glueing-construction described in this paper makes use of two generalized quadrangles with a spread in each of them and yields a partial linear space with special properties. We study the conditions under which glueing will give a near hexagon. These near hexagons satisfy the nice property that every two points at distance 2 are contained in a quad. We characterize the class of the “glued n...
متن کاملOn Q-polynomial regular near 2d-gons
We discuss thick regular near 2d-gons with a Q-polynomial collinearity graph. For d ≥ 4, we show that apart from Hamming near polygons and dual polar spaces there are no thick Q-polynomial regular near polygons. We also show that no regular near hexagons exist with parameters (s, t2, t) equal to (3, 1, 34), (8, 4, 740), (92, 64, 1314560), (95, 19, 1027064) or (105, 147, 2763012). Such regular n...
متن کاملThe classification of the slim dense near octagons
We classify all dense near octagons with three points on each line.
متن کاملExtended near hexagons and line systems
In this paper we study extended near hexagons, and classify a class of line systems in which two lines are either perpendicular, or make an angle a with cos a 1⁄4G1=3. Among the examples we encounter a set of 2300 lines in R related to the second Conway group Co2 and a set of 2048 lines in R related to the group 21þ11 : M24. These line systems carry the structure of an extended near hexagon. Th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Discrete Mathematics
دوره 308 شماره
صفحات -
تاریخ انتشار 2008