Geometry — von Staudt’s Point of View: Proceedings of the NATO Advanced Study Institute held at Bad Windsheim, West Germany, July 21—August 1,1980 (Nato Science Series C:)

ISBN 10: 940098491X / ISBN 13: 9789400984912

Published by Springer, 2011

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Bibliographic Details

• Title: Geometry ? von Staudt?s Point of View: Proceedings of the NATO Advanced Study Institute held at Bad Windsheim, West Germany, July 21?August 1,1980 (Nato Science Series C:)
• Publisher: Springer
• Publication Date: 2011
• Language: English
• ISBN 10: 940098491X
• ISBN 13: 9789400984912
• Binding: Soft cover
• Condition: New

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Synopsis

Ever since F. Klein designed his "Erlanger programm", geometries have been studied in close connection with their groups of automorphisms. It must be admitted that the presence of a large automorphismgroup does not always have strong implications for the incidence-th- retical behaviour of a geometry. For exampl O. H. Kegel and A. Schleiermacher [Geometriae Dedicata 2, 379 - 395 (1974)J constructed a projective plane with a transitive action of its collineation group on quadrangles, in which, nevertheless every four points generate a free subplane. However, there are several important special classes of geometries, in which strong implications are present. For instance, every finite projective plane with a doubly transitive collineation group is pappian (Theorem of Ostrom-Wagner), and every compact connected projective plane with a flag-transitive group of continuous collineations is a Moufang plane (H. Salzmann, Pac. J. Math., 217 - 234 (1975)]. Klein's point of view has been very useful for numerous incidence structures and has established an intimate connection between group theory and geometry vii P. Plaumann and K. Strambach (eds. ), Geometry - von Staudt's Point of View, vii-xi. Copyright (c) 1981 by D. Reidel Publishing Company. viii PREFACE 1. 1:1ich is a guidepost for every modern t: reat: ment of geometry. A few decades earlier than Klein's proposal, K. G. Ch. von Staudt stated a theorem which indicates a different point of view and is nowadays sometimes called the "Fundamental Theorem of Projective Geometry".