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In this paper, we characterize isomorphisms of generalized polygons (in particular automorphisms) by maps on flags which preserve a certain fixed distance. In Part II, we consider maps on point and/or lines. Exceptions give rise to interesting properties, which on their turn have some nice applications. MSC 2000: 51E12

In this paper, we characterize isomorphisms of generalized polygons (in particular automorphisms) by maps on points and/or lines which preserve a certain fixed distance. In Part I, we considered maps on flags. Exceptions give rise to interesting properties, which on their turn have some nice applications. MSC 2000: 51E12

- Eline Govaert, Hendrik Van Maldeghem
- Discrete Mathematics
- 2003

We generalize the notion of a semi-a$ne plane to structures with higher girth n. We prove that, in the 1nite case, for n odd, and with an additional assumption also for n even, these geometries, which we call forgetful n-gons, always arise from (1nite) generalized n-gons by ‘forgetting’ lines. c © 2003 Elsevier B.V. All rights reserved.

We characterize the dual of the generalized hexagons naturally associated to the groups G2(q) and 3D4(q) by looking at certain configurations, and also by considering intersections of traces. For instance, the dual of a generalized hexagon F of finite order (s, t) is associated to the Chevaliey groups mentioned above if and only if the intersection of any… (More)

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