Half Moufang implies Moufang for finite generalized quadrangles
type: Item
instance of: scholarly article
title: Half Moufang implies Moufang for finite generalized quadrangles
zbMATH Open document ID: 0708.51010
DOI: 10.1007/BF01232260
author: Stanley E. Payne
author: Joseph A. Thas
author: Hendrik Van Maldeghem
published in: Inventiones Mathematicae
publication date: 1991-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143907
review text: Let \({\mathcal S}=(P,B,I)\) be a finite generalized quadrangle of order \((s,t)\), \(s>1\), \(t>1\). A panel of \({\mathcal S}\) is an ordered triple \((x,L,y)\) where \(x\) and \(y\) are distinct points incident with the line \(L\), or an ordered triple \((L,p,M)\) where \(L\) and \(M\) are distinct lines incident with the point \(P\). For a given panel \((x,L,y)\), let \(H(x,L,y)\) be the group of all collineations of \({\mathcal S}\) which fix \(x\) and \(y\) linewise and \(L\) pointwise. We say the panel \((x,L,y)\) is Moufang provided \(| H(x,L,y)| =s\). For a panel \((L,p,M)\), the group \(H(L,p,M)\) is defined in a dual manner. And \((L,p,M)\) is Moufang provided \(| H(L,p,M)| =t\). If every panel of \({\mathcal S}\) is Moufang, then by a theorem of Fong and Seitz, \({\mathcal S}\) must be isomorphic to one of the so-called classical or dual classical generalized quadrangles. The main result of this paper is that if every panel of one type is Moufang, then all panels are Moufang.
Mathematics Subject Classification ID: 51E12
zbMATH DE Number: 4163621
zbMATH Keywords: finite generalized quadrangle
MaRDI profile type: Publication
cites work: Groups with a (B,N)-pair of rank 2. I
cites work: Q3344217
cites work: Q4117037
OpenAlex ID: W2044106975
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description: scientific article; zbMATH DE number 4163621