One-point extensions of polar spaces
type: Item
instance of: scholarly article
title: One-point extensions of polar spaces
zbMATH Open document ID: 0732.51005
DOI: 10.1016/S0195-6698(13)80038-8
author: P. H. Fisher
author: Tim Penttila
published in: European Journal of Combinatorics
publication date: 1990-01-01T00:00:00Z
review text: The authors combinatorially characterize one-point extensions of finite, thick, non-degenerate polar spaces of rank at least 3. It is proved that in this case the polar space is defined over GF(2) and an explicit construction of the one-point extension is given. This gives a more elementary proof (not involving group-theoretic methods) of F. Buekenhout's result on the uniqueness of one-point extensions of classical polar spaces [\textit{F. Buekenhout}, Geom. Dedicata 6, No.1, 13- 21 (1977; Zbl 0363.05056)]. Using their characterization the authors further show that the automorphism group of a one-point extension of a finite, thick, non-degenerate polar space of rank at least 3 is a one- point extension of the automorphism group of the polar space.
Mathematics Subject Classification ID: 51A50
Mathematics Subject Classification ID: 51E24
zbMATH DE Number: 4210938
zbMATH Keywords: polar space
zbMATH Keywords: one-point extension
zbMATH Keywords: automorphism group
reviewed by: Günter F. Steinke
MaRDI profile type: Publication
cites work: Extensions of polar spaces and the doubly transitive symplectic groups
cites work: Locally polar spaces and related rank 3 groups
cites work: On the foundations of polar geometry
cites work: Q3344217
cites work: Q3736447
cites work: Buildings of spherical type and finite BN-pairs
full work available at URL: s0195-6698(13)80038-8
OpenAlex ID: W2084914966
description: scientific article; zbMATH DE number 4210938