A Finite Generalized Hexagon Admitting a Group Acting Transitively on Ordered Heptagons is Classical
✍ Scribed by H. Van Maldeghem
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 412 KB
- Volume
- 75
- Category
- Article
- ISSN
- 0097-3165
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✦ Synopsis
Let 1 be a thick finite generalized hexagon and let G be a group of automorphisms of 1. If G acts transitively on the set of non-degenerate ordered heptagons, then 1 is one of the Moufang hexagons H(q) or 3 H(q) associated to the Chevalley groups G 2 (q) or 3 D 4 (q) respectively, or their duals; and G contains the corresponding Chevalley group. Moreover, we show that no thick generalized octagon admitting a group acting transitively on the set of ordered nonagons (enneagons) can exist. This completes the determination of all finite thick generalized n-gons, n 3, with a group acting transitively on the set of ordered (n+1)-gons with elementary methods. Because we do not use the classification of the finite simple groups, from which these results also follow.
1996 Academic Press, Inc.
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(GP3) If the distance in the incidence graph between two elements (points and lines) v, w is strictly smaller than n, then there is a unique article no.