Abstract
This paper is intended to be a first step towards the classification of finite flag-transitive geometries of rank 3 with affine planes and dual affine point-residues. We describe those of diameter 1. In the case of diameter > 1, we describe minimal quotients, assuming that the number of lines through two points is large enough.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
BAUMEISTER,B.:Fahnentransitive Rang 3 Geometrien, die lokal vollständige Graphen rind, Diplomarbeit, Freie Universität Berlin, 1992.
BUEKENHOUT,F. and PASINI,A.:Finite Diagram Geometries Extending Buildings, Chapter 22 of “Handbook of Incidence Geometry” (F. Buekenhout ed.), Kluwer, (to appear).
BUEKENHOUT,F., HUYBRECHTS,C. and PASINI,A.:Parallelism in diagram geometry, (in preparation).
DELFRA,A. and PASINI,A.:L.A n .L * Geometries (submitted).
DEMBOWSKI,P.: “Finite Geometries”, Springer Verlag, Berlin, 1968.
HUYBRECHTS,C. and PASINI,A.:A report of Flag-transitive L.L *-geometries, (in preparation).
LEFEVRE-PERCSY,C. and VAN NYPELSEER,L.:Finite rank 3 geometries with affine planes and dual affine point residues, Discrete Math., 84 (1990), 161–167.
PASINI,A.: “An Introduction to Diagram Geometry”, Oxford U. P., (to appear).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Del Fra, A., Pasini, A. On Af.Af* geometries. J Geom 54, 15–29 (1995). https://doi.org/10.1007/BF01222849
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01222849