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Zbl 0565.05014
Cohen, A.M.; Tits, Jacques
On generalized hexagons and a near octagon whose lines have three points. (English)
[J] Eur. J. Comb. 6, 13-27 (1985). ISSN 0195-6698

The authors prove that the only generalized hexagons of order (2,2) are the classical one and its dual (both associated with the group $G\sb 2(2))$. They also prove the uniqueness of the generalized hexagon of order (2,8), associated with ${}\sp 3D\sb 4(2)$, and of the near octagon of order (2,4;0,3), associated with the Hall-Janko group. The treatment of the case (2,8) is facilitated by the use of results of Ronan and Timmesfeld. The arguments for all three cases are presented in terms of the (distance-regular) incidence graphs associated with the geometries. A central theme is the identification of subgraphs which are isomorphic to "2-covers" of the n-cube.
[D.A.Drake]

MSC 2000:: *05B30 Other designs, configurations
20D08 Simple groups: sporadic finite groups
51M20 Regular figures in space
05B25 Finite geometries (combinatorics)
51D20 Combinatorial geometries

Keywords: distance-regular graph; regulus condition; generalized hexagons; near octagon; Hall-Janko group

Cited in: Zbl 0979.51002

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