In this article, the finite translation planes which are quadratic extensions of flag-transitive subplanes are classified as either Desarguesian or Hall.
Flag-transitive extensions ofCngeometries
โ Scribed by A. Del Fra; D. Ghinelli; T. Meixner; A. Pasini
- Publisher
- Springer
- Year
- 1991
- Tongue
- English
- Weight
- 1010 KB
- Volume
- 37
- Category
- Article
- ISSN
- 0046-5755
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โฆ Synopsis
We consider locally Cn-geometries where all planes are circular spaces (i.e., complete graphs). We call them extensions of Cn-geometries or (c.Cn) geometries, for short. We give a classification of finite flag-transitive (c.Cn) geometries when n/> 3. A classification is given also in the case of n = 2 under the hypothesis that residues of points are thick classical generalized quadrangles.
๐ SIMILAR VOLUMES
Pasini, A., Flag-transitive C,-geometries, Discrete Mathematics 117 (1993) 169-182. We obtain conditions on the structure and the parameters of an anomalous finite thick flagtransitive C,-geometry.