Finite locally generalized quadrangles with affine planes
type: Item
instance of: scholarly article
title: Finite locally generalized quadrangles with affine planes
zbMATH Open document ID: 0768.51004
DOI: 10.1016/0195-6698(92)90003-I
published in: European Journal of Combinatorics
publication date: 1993-02-03T00:00:00Z
review text: The first author and \textit{A. Pasini} [Eur. J. Comb. 13, No. 1, 39-57 (1992; Zbl 0749.51005)] characterized standard quotients of affine polar spaces of at least rank 4 (an affine polar space is a polar space with a geometric hyperplane removed; a standard quotient of it is a quotient w.r.t. to a group ``fixing the deleted geometric hyperplane'' pointwise). The main result of the paper under review is to extend this result to the rank 3 case (but only in the finite case). Basically, the author shows that every connected finite partial linear space containing affine planes and such that the set of lines and affine planes through any point forms a generalized quadrangle, is a standard quotient of a finite rank 3 affine polar space.
Mathematics Subject Classification ID: 51E12
Mathematics Subject Classification ID: 51A50
zbMATH DE Number: 109274
zbMATH Keywords: affine polar space
zbMATH Keywords: standard quotient
zbMATH Keywords: generalized quadrangle
author: Hans Cuypers
reviewed by: Hendrik Van Maldeghem
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 109274