Please use this identifier to cite or link to this item: http://dx.doi.org/10.18419/opus-6944
Authors: Hähl, Hermann
Title: Homologies and elations in compact, connected projective planes
Issue Date: 1981
metadata.ubs.publikation.typ: Zeitschriftenartikel
metadata.ubs.publikation.source: Topology and its application 12 (1981), S. 49-63. URL http://dx.doi.org./10.1016/0166-8641(81)90029-8
URI: http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-41213
http://elib.uni-stuttgart.de/handle/11682/6961
http://dx.doi.org/10.18419/opus-6944
Abstract: In a compact, connected topological projective plane, let Ω be a closed Lie subgroup of the group of all axial collineations with a fixed axis A. We compare the set З\A consisting of the centres of all non-identical homologies in Ω to orbits of the group Ω[A] of all elations contained in Ω and of its connected component θ = (Ω[A])1. It is shown that З\A is the union of at most countably many θ-orbits; moreover, З\A turns out to be a single θ-orbit whenever the connected component of Ω contains non-identical homologies. This result is analogous to a well-known theorem of André for finite planes. It has numerous consequences for the structure of collineation groups of compact, connected projective planes.
Appears in Collections:15 Fakultätsübergreifend / Sonstige Einrichtung

Files in This Item:
File Description SizeFormat 
hae12.pdf2,74 MBAdobe PDFView/Open


Items in OPUS are protected by copyright, with all rights reserved, unless otherwise indicated.