On restrictions of automorphism groups of compact projective planes to subplanes
type: Item
instance of: scholarly article
title: On restrictions of automorphism groups of compact projective planes to subplanes
zbMATH Open document ID: 0765.51014
DOI: 10.1007/BF03323089
author: Theo Grundhöfer
author: Markus Stroppel
published in: Results in Mathematics
publication date: 1992-09-27T00:00:00Z
review text: The authors show that the restriction of a compact projective plane to a closed Baer subplane, or to an open subgeometry, is a quotient mapping. This contrasts with restrictions to arbitrary subgeometries. In the proof, they investigate lineations in towers of Baer subplanes. No connectedness assumptions are needed. The notions and the necessity of the assumptions are illustrated by examples.
reviewed by: Hansjoachim Groh
Mathematics Subject Classification ID: 51H10
zbMATH DE Number: 62172
zbMATH Keywords: automorphism
zbMATH Keywords: compact projective plane
zbMATH Keywords: closed Baer subplane
zbMATH Keywords: open subgeometry
zbMATH Keywords: quotient mapping
MaRDI profile type: Publication
cites work: Collinearity-preserving functions between Desarguesian planes
cites work: Einige Sätze über topologische Gruppen
cites work: Automorphism groups of compact projective planes
cites work: Automorphismengruppen von lokalkompakten zusammenhängenden Quasikörpern und Translationsebenen
cites work: Dimension der Bahnen lokal kompakter Gruppen
cites work: Vierdimensionale stabile Ebenen
cites work: Topology and dimension of stable planes: On a conjecture of H. Freudenthal.
cites work: Compact 8-dimensional projective planes with large collineation groups
cites work: Automorphismengruppen 8-dimensionaler Ternärkörper
cites work: Kompakte, 8-dimensionale projektive Ebenen mit großer Kollineationsgruppe
cites work: Baer-Kollineationsgruppen der klassischen projektiven Ebenen
cites work: Q4003004
description: scientific article; zbMATH DE number 62172