Linear spaces on v points with v-2 mutually intersecting long lines
type: Item
instance of: scholarly article
title: Linear spaces on v points with v-2 mutually intersecting long lines
zbMATH Open document ID: 0705.51007
DOI: 10.1007/BF01230362
author: Pia Maria Lo Re
author: Paola De Vito
author: Nicola Melone
published in: Journal of Geometry
publication date: 1990-01-01T00:00:00Z
review text: We assume familiarity with the concepts of finite linear spaces. In this paper it is proved that a finite linear space \textbf{L} such that (1) any two long lines intersect each other, (2) \(b_ n=v-2\), where \(b_ n\) is the number of long lines and v is the number of points of \textbf{L}, is one of the following structures: (i) a projective plane of order n-1 with two extra points, (ii) the Fano quasi-plane with a long line broken into three short ones, (iii) the finite linear space obtained from a projective plane of order n-1 by breaking up a line into a linear space and with an extra point, (iv) the punctured Fano plane, (v) the finite linear space obtained from a projective plane of order n-1 by breaking up two lines into two linear spaces. For the definition of these notions, and related concepts, we refer the reader also to \textit{P. de Witte} [J. Reine Angew. Math. 288, 66-73 (1976; Zbl 0333.50009)].
Mathematics Subject Classification ID: 51D20
Mathematics Subject Classification ID: 51E20
zbMATH DE Number: 4157367
zbMATH Keywords: affine plane
zbMATH Keywords: finite linear space
zbMATH Keywords: projective plane
reviewed by: Giorgio Faina
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4157367