Abstract
Desarguesian projective planes of square order are characterized by the property that every quadrangle lies on a unique Baer subplane.
Similar content being viewed by others
References
Beutelspacher A.: Projective planes (Chap. 4). In: Buekenhout F. (ed.) Handbook of Incidence Geometry, pp. 107–136. North-Holland, Amsterdam (1995).
Blokhuis A., Sziklai P.: On planes of order p 2 in which every quadrangle generates a subplane of order p. Geom. Dedicata 79, 341–347 (2000)
Dembowski P.: Finite Geometries. Springer, Berlin (1997) (reprint of the 1968 edition).
Grundhöfer T.: The groups of projectivities of finite projective and affine planes. Ars Combin 25, 269–275 (1988)
Killgrove R.B.: Completions of quadrangles in projective planes. Can. J. Math 16, 63–76 (1964)
Mac Innes C. R.: Finite planes with less than eight points on a line. Am. Math. Mon 14, 171–174 (1907)
Müller P., Nagy G.P.: A note on the group of projectivities of finite projective planes. Innov. Incidence Geom 6/7, 291–294 (2007/08)
Veblen O., Wedderburn J.H.M.: Non-Desarguesian and non-Pascalian geometries. Trans. Am. Math. Soc 8, 379–388 (1907)
Author information
Authors and Affiliations
Corresponding author
Additional information
This is one of several papers published together in Designs, Codes and Cryptography on the special topic: “Geometric and Algebraic Combinatorics”.
Rights and permissions
About this article
Cite this article
Kantor, W.M., Penttila, T. Planes in which every quadrangle lies on a unique Baer subplane. Des. Codes Cryptogr. 65, 157–161 (2012). https://doi.org/10.1007/s10623-011-9567-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10623-011-9567-0