On delta spaces satisfying Pasch's axiom
type: Item
instance of: scholarly article
title: On delta spaces satisfying Pasch's axiom
zbMATH Open document ID: 0839.51004
DOI: 10.1007/BF01224040
author: Hans Cuypers
published in: Journal of Geometry
publication date: 1996-06-19T00:00:00Z
review text: Connected partial linear spaces all of whose planes are projective are projective planes or Desarguesian projective spaces as follows by the classical result of Veblen and Young. The author has completely classified delta spaces containing only dual affine planes in the paper `Symplectic geometries, transvection groups and modules' (to appear in J. Comb. Theory, Ser. A) for the case that all lines have more than three points. The remaining cases have been classified by \textit{J. I. Hall} [Proc. Lond. Math. Soc., III. Ser. 58, No. 1, 89-111 (1989; Zbl 0673.20015)]. The main theorem of the present article with the result given above settles the classification of delta spaces in which all planes are projective or dual affine, up to the determination of projective and dual affine planes.
Mathematics Subject Classification ID: 51A45
zbMATH DE Number: 785147
zbMATH Keywords: Pasch's axiom
zbMATH Keywords: delta spaces
Wikidata QID: Q114018458
reviewed by: Pavel Burda
MaRDI profile type: Publication
cites work: Symplectic geometries, transvection groups, and modules
cites work: Affine Grassmannians
cites work: Finite geometries which contain dual affine planes
cites work: The hyperbolic lines of finite symplectic spaces
cites work: Graphs, Geometry, 3-Transpositions, and Symplectic F 2 -Transvection Groups
cites work: Geometric hyperplanes of embeddable Grassmannians
cites work: Q5334781
full work available at URL: https://doi.org/10.1007/bf01224040
OpenAlex ID: W2005877688
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description: scientific article; zbMATH DE number 785147