A connection between Fano configurations and Minkowski planes of odd order
type: Item
instance of: scholarly article
title: A connection between Fano configurations and Minkowski planes of odd order
zbMATH Open document ID: 0673.51005
DOI: 10.1007/BF00182122
author: Jan Jakóbowski
published in: Geometriae Dedicata
publication date: 1989-01-01T00:00:00Z
review text: Let \(M\) be a Minkowski plane and \(p{\bar \in}M\). Which projective planes are possible for being the projective closure \(\overline{M_p}\) of the affine derivation \(M_p\)? The closure of the circles of \(M\) not containing \(p\) are ovals through two special points of \(\overline{M_p}\). The author shows that for a plane of odd order those two points can not lie in a projective subplane \(\overline{M_p}\) of order two. This theorem can be applied to the Hughes plane of order 9 in which any pair of different points is contained in a subplane of order two.
Mathematics Subject Classification ID: 51B20
Mathematics Subject Classification ID: 51E15
Mathematics Subject Classification ID: 51E25
zbMATH DE Number: 4101975
zbMATH Keywords: Minkowski plane
zbMATH Keywords: Hughes plane
reviewed by: Herbert Hotje
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00182122
OpenAlex ID: W162213283
description: scientific article; zbMATH DE number 4101975