The cyclic parallelism of PG(3,5)
type: Item
instance of: scholarly article
title: The cyclic parallelism of PG(3,5)
zbMATH Open document ID: 0907.51004
published in: European Journal of Combinatorics
publication date: 1999-02-18T00:00:00Z
review text: A spread of the projective space \(P = \text{PG}(3,q)\) is a set of \(q^2+1\) pairwise non-intersecting lines of \(P\). A parallelism of \(P\) is a family of \(q^2+q+1\) spreads of \(P\) which partition the set of lines of \(P\). A parallelism is called cyclic, if there is a collineation of \(P\) of order \(q^2+q+1\) that permutes its spreads in a cyclic way. A parallelism is called regular, if any of its spreads is regular. Up to now, no example of a regular parallelism of \(P\) was known. In the paper under review the author determines (by the use of a computer) all cyclic parallelisms of \(\text{PG} (3,5)\). Up to projective equivalence, there are 45 cyclic parallelisms of \(\text{PG} (3,5)\), two of them being regular.
Mathematics Subject Classification ID: 51E23
zbMATH DE Number: 1199945
zbMATH Keywords: projective space
zbMATH Keywords: cyclic parallelism
zbMATH Keywords: PG(3,5)
author: Alan R. Prince
MaRDI profile type: Publication
full work available at URL: eujc.1997.0204
OpenAlex ID: W2001445867
DOI: 10.1006/EUJC.1997.0204
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description: scientific article; zbMATH DE number 1199945