Baer subplanes generated by collineations between pencils of lines
type: Item
instance of: scholarly article
title: Baer subplanes generated by collineations between pencils of lines
zbMATH Open document ID: 1117.51009
DOI: 10.1007/BF02875746
author: Giorgio Donati
author: Nicola Durante
publication date: 2007-02-02T00:00:00Z
review text: In this paper the authors obtain an interesting results on special Baer subplanes in \(\text{PG}(2,q^{2})\): Let \(\;l_{\infty }\) be a line of \(\text{PG}(2,q^{2})\) and A be an affine Baer subplane of \(\text{PG}(2,q^{2})\backslash l_{\infty }\). Then there exist two distinct point \(A\),\(B\) on \(l_{\infty }\) such that A\(\cup\;l_{\infty } \) is the set of points of intersection of corresponding lines under an \( \alpha _{F}\)-collineation between the pencils of lines with vertices \(A\), \(B\). Moreover A\(\cup\;l_{\infty }\) may be represented by the equation \(x_{3}(x_{1}x_{3}^{q-1}-x_{2}^{q})=0\).
Mathematics Subject Classification ID: 51E20
zbMATH DE Number: 5121509
reviewed by: Basri Çelik
MaRDI profile type: Publication
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published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 5121509