Recently there has been renewed interest in a class of geometries introduced by Tits many years ago. Part of this interest stems from Tits' paper [-6] which characterizes buildings as the simply connected geometries with Coxeter diagram in which all residues of type C 3 and H 3 are buildings. Defin
Geometries of type Cnand F4with flag-transitive automorphism groups
β Scribed by Antonio Pasini
- Publisher
- Springer
- Year
- 1988
- Tongue
- English
- Weight
- 686 KB
- Volume
- 25
- Category
- Article
- ISSN
- 0046-5755
No coin nor oath required. For personal study only.
β¦ Synopsis
ABSTRACTΒ°
Let F be a finite thick geometry of type C n (n ~ 4) or F4. We prove that F is a building iff Aut(F) is flag-transitive.
π SIMILAR VOLUMES
Examples 1.1. (Desarguesian affine spaces). Here S is an affine space AG n (q), where n 2 and q n = p d ; we have G 0 1L n (q), and one of the following holds:
The classification of the finite simple groups has shown that most of the finite simple groups possess a natural representation as a flag transitive automorphism group of a suitable geometry; conversely, a successful treatment of larger classes of geometries can often be ensured only under additiona
A graph X is said to be 1 2 -transitive if its automorphism group acts transitively on the sets of its vertices and edges but intransitively on the set of its arcs. A construction of a 1 2 -transitive graph of valency 4 and girth 6 with a nonsolvable group of automorphism is given.
According to Mathon and Rosa [The CRC handbook of combinatorial designs, CRC Press, 1996] there is only one known symmetric design with parameters (69, 17, 4). This known design is given in Beth, Jungnickel, and Lenz [Design theory, B. I. Mannheim, 1985]; the Frobenius group F39 of order 39 acts on