Subquadrangles of order \(s\) of generalized quadrangles of order (\(s,s^{2}\)). II
type: Item
instance of: scholarly article
title: Subquadrangles of order \(s\) of generalized quadrangles of order (\(s,s^{2}\)). II
zbMATH Open document ID: 1050.51005
published in: Journal of Combinatorial Theory. Series A
publication date: 2004-08-06T00:00:00Z
review text: The authors investigate subquadrangles of order \(s\) of generalized quadrangles of order \((s,s^2)\), \(s\) odd. The case of even \(s\) is considered in [J. Comb. Theory, Ser. A 106, No. 1, 15--32 (2004; see the review above)]. Suppose that \(Q'\) is a subquadrangle of order \(s\) of a generalized quadrangle of order \((s,s^2)\), \(s\) odd. The authors show that if \(Q\) is a translation generalized quadrangle, such that the corresponding egg has a good element \(\pi\), then \(Q'\) is isomorphic to \(Q(4,s)\) and either \(Q\) is isomorphic to \(Q(5,s)\) or \(Q'\) is one of the \(s^3+s^2\) subquadrangles of order \(s\) through the line \(\pi\) of \(Q\). If \(Q\) is a dual flock GQ and \(Q'\) contains the line \(L^\ast\) corresponding with the base point \((\infty)\) of the flock GQ \(Q^D\), then \(Q^D\) is a Kantor semifield flock GQ, \(Q'\) is isomorphic to \(Q(4,s)\) and either \(Q\) is isomorphic to \(Q(5,s)\) or \(Q'\) is one of the \(s^3+s^2\) subquadrangles of order \(s\) containing the line \(L^\ast\). The authors also provide a characterization of the Kantor semifield flock GQ in terms of the net which can be defined on the base point \((\infty)\).
reviewed by: Bart De Bruyn
Mathematics Subject Classification ID: 51E12
zbMATH DE Number: 2081938
zbMATH Keywords: generalized quadrangles
zbMATH Keywords: egg
zbMATH Keywords: flock
author: Matthew Brown
author: Joseph A. Thas
MaRDI profile type: Publication
full work available at URL: j.jcta.2003.12.007
OpenAlex ID: W1966421268
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DOI: 10.1016/J.JCTA.2003.12.007
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description: scientific article; zbMATH DE number 2081938