The classification of subplane covered nets
type: Item
instance of: scholarly article
title: The classification of subplane covered nets
zbMATH Open document ID: 0855.51002
author: Norman L. Johnson
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 1996-03-17T00:00:00Z
full work available at URL: https://eudml.org/doc/229580
review text: A net is called subplane covered if for any two distinct collinear points there is a subplane which contains the two points and whose infinite points are the infinite points of the net. Extending his results on the structure of derivable nets, the author proves that every subplane covered net can be obtained from a projective space \(\Sigma\) and a subspace \(N\) of codimension 2 as follows. Points of the net are the lines of \(\Sigma\) which do not intersect \(N\) and lines of the net are the points of \(\Sigma\) not contained in \(N\). The subplanes of the net correspond to the subplanes of \(\Sigma\) which intersect \(N\) in precisely one point.
reviewed by: Norbert Knarr
Mathematics Subject Classification ID: 51A15
Mathematics Subject Classification ID: 51A45
zbMATH DE Number: 856771
zbMATH Keywords: pseudo-regulus net
zbMATH Keywords: subplane
zbMATH Keywords: net
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 856771