On generalized André planes of dimension \(2(2n+1)\)
type: Item
instance of: scholarly article
title: On generalized André planes of dimension \(2(2n+1)\)
zbMATH Open document ID: 0542.51007
DOI: 10.1007/BF02844413
author: A. Caggegi
publication date: 1984-01-01T00:00:00Z
review text: Let P be a proper generalized André plane (i.e. P is neither a Desarguesian plane nor a Hall plane). If P is finite, it is known that P has the following property: (*) there exist in P two special pencils of parallel lines fixed or exchanged by every collineation. It was an open question whether this property depends on the finite order or not. The author shows that P (not necessarily finite) has again the property (*) if P is of odd dimension and its homology groups fixing the above pencils have order \(\leq 2\). Yet the author shows in a more recent article (to appear in Geom. Dedicata) that this pattern cannot be expected to hold in the case of even dimension. In fact he gives an example of an (infinite) generalized André plane of dimension 4 which does not have the property (*).
Mathematics Subject Classification ID: 51A40
zbMATH DE Number: 3861912
zbMATH Keywords: generalized André plane
zbMATH Keywords: pencils
zbMATH Keywords: collineation
MaRDI profile type: Publication
cites work: Über verallgemeinerte Moulton-Ebenen
cites work: Piani di Andre generalizzati
cites work: Q4157627
cites work: Die Kollineationsgruppe verallgemeinerter Andre-Ebenen mit Homologien
cites work: Collineation Groups of Generalized André Planes
cites work: Q3891315
cites work: A characterization of generalized Andre planes
cites work: Eine Klasse unendlicher verallgemeinerter Andre-Ebenen
full work available at URL: https://doi.org/10.1007/bf02844413
OpenAlex ID: W2326643977
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 3861912