Please use this identifier to cite or link to this item: http://dx.doi.org/10.18419/opus-6944
|Title:||Homologies and elations in compact, connected projective planes|
|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|
|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|
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