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http://dx.doi.org/10.18419/opus-6944
Autor(en): | Hähl, Hermann |
Titel: | Homologies and elations in compact, connected projective planes |
Erscheinungsdatum: | 1981 |
Dokumentart: | Zeitschriftenartikel |
Erschienen in: | 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 |
Zusammenfassung: | 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. |
Enthalten in den Sammlungen: | 15 Fakultätsübergreifend / Sonstige Einrichtung |
Dateien zu dieser Ressource:
Datei | Beschreibung | Größe | Format | |
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hae12.pdf | 2,74 MB | Adobe PDF | Öffnen/Anzeigen |
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