Extended 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 ¼ G1=3. Among the examples we encounter a set of 2300 lines in R 23 related to the second Conway group Co2 and a set of 2048 lines in R 24 related to the group 2 1þ11 : M24. These line systems carry the struc- ture of an extended near hexagon. The other line systems and extensions of near hexagons under consideration in this paper are all subsystems of these.

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