Abstract
It is shown in this paper that a pair of points contained in a Fano configuration in a projective plane of odd order cannot induce a Minkowski plane. From this result we derive that no pair of points in the Hughes plane of order 9 can induce a Minkowski plane.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Dembowski, P., Finite Geometries, Springer-Verlag, Berlin, Heidelberg, New York, 1968, pp. 115–137.
Denniston, R. H. F., ‘Subplane of the Hughes Plane of Order 9’, Proc. Camb. Phil. Soc. Math. Phys. Sci. 64 (1968), 589–598.
Heise, W. and Karzel H., ‘Symmetrische Minkowski Ebenen’, J. Geom. 3 (1973), 5–20.
Hughes, D. R., ‘A Class of Non-Desarguesian Projective Planes’, Canad. J. Math. IX, No 3 (1957), 378–388.
Percsy, N., ‘Finite Minkowski Planes in which every Circle-Symmetry is an Automorphism’, Geom. Dedicata 10 (1981), 269–282.
Quist, B., ‘Some Remark Concerning Curves of the Second Degree in a Finite Plane’, Ann. Acod. Sci Fenn. 134 (1952), 1–27.
Rahilly, A. J., ‘The Existence of Fano Subplanes in Generalized Hall Planes’, J. Austral. Math. Soc. 16 (1973), 234–238.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Jakóbowski, J. A connection between Fano configurations and Minkowski planes of odd order. Geom Dedicata 29, 221–226 (1989). https://doi.org/10.1007/BF00182122
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00182122