A stabilizer Lemma for translation generalized quadrangles
type: Item
instance of: scholarly article
title: A stabilizer Lemma for translation generalized quadrangles
zbMATH Open document ID: 1108.51008
author: Koen Thas
published in: European Journal of Combinatorics
publication date: 2006-12-07T00:00:00Z
review text: Let \(F\) be a semifield flock of the finite projective space \(\text{PG}(3,q^n)\), where \(q\) is odd. The author proves that \(F\) is linear if the order of the automorphism group of \(F\) is divisible by \(q^n (q^n +1)\). As a consequence, he obtains the following result for a certain class of translation generalized quadrangles \(S\) of order \((s, s^2)\) where \(s\) is odd: if the collineation group of \(S\) acts transitively on the subquadrangles of \(S\) of order \(s\), then \(S\) is isomorphic to the classical generalized quadrangle \(Q(5,s)\).
reviewed by: Theo Grundhöfer
Mathematics Subject Classification ID: 51E12
zbMATH DE Number: 5077681
zbMATH Keywords: flock
zbMATH Keywords: subquadrangle
MaRDI profile type: Publication
full work available at URL: j.ejc.2005.10.008
OpenAlex ID: W2071032904
Wikidata QID: Q124804723
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DOI: 10.1016/J.EJC.2005.10.008
description: scientific article; zbMATH DE number 5077681