On regular parallelisms in PG(3,q)
type: Item
instance of: scholarly article
title: On regular parallelisms in PG(3,q)
zbMATH Open document ID: 0546.51003
DOI: 10.1016/0012-365X(84)90003-7
published in: Discrete Mathematics
publication date: 1984-01-01T00:00:00Z
review text: A parallelism of \(S_ 3=PG(3,q)\) is a set \({\mathcal P}\) of \(q^ 2+q+1\) spreads such that no two distinct spreads of \({\mathcal P}\) have a line in common. A spread is said to be regular if for any 3 distinct lines of the spread the regulus (that is, one ruling of a nondegenerate hyperbolic quadric in \(S_ 3)\) determined by these 3 lines is contained in the spread. If all spreads of \({\mathcal P}\) are regular, then \({\mathcal P}\) is called a regular parallelism of \(S_ 3\). The author proves that for odd q there are no regular parallelisms of \(S_ 3\).
Mathematics Subject Classification ID: 51A40
Mathematics Subject Classification ID: 51A30
Mathematics Subject Classification ID: 51E20
zbMATH DE Number: 3870093
zbMATH Keywords: projective space
zbMATH Keywords: spread
zbMATH Keywords: regular parallelism
author: Guglielmo Lunardon
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3870093