\(m\)-parallelisms
type: Item
instance of: scholarly article
title: \(m\)-parallelisms
zbMATH Open document ID: 1016.51011
DOI: 10.1155/S0161171202007500
author: Norman L. Johnson
author: Rolando J. Pomareda
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2003-01-13T00:00:00Z
full work available at URL: https://eudml.org/doc/50167
review text: In [\textit{N. L. Johnson}, `Subplane covered nets', Pure and Applied Mathematics, vol. 222, Marcel Dekker, New York (2000; Zbl 0954.51002)] a group-theoretic construction of a class of parallelisms in \(PG(3,K)\), \(K\) a field admitting a quadratic extension, is given. Such parallelisms enjoy the property that there exist a unique Pappian spread \(\Sigma_1\) and a collineation group \(G\) of the parallelism, which is also the full central collineation group of \(\Sigma_1\) with fixed axis \(\ell\). Also \(G\) is transitive on the remaining spreads of the parallelisms, and all spreads involved are Hall spreads. Here the authors give a generalization of the above construction, using the full central collineation group \(G\) of an associated Pappian spread, choosing \(m\) Pappian spreads instead of a second Pappian spread, sharing a regulus with the original Pappian spread. They construct this way many parallelisms.
Mathematics Subject Classification ID: 51E23
Mathematics Subject Classification ID: 51A40
zbMATH DE Number: 1852878
zbMATH Keywords: Hall spreads
zbMATH Keywords: parallelisms
zbMATH Keywords: skewfields
reviewed by: Antonio Cossidente
MaRDI profile type: Publication
OpenAlex ID: W4244470771
description: scientific article; zbMATH DE number 1852878