Geometry — von Staudt’s Point of View:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1981
|
| Schriftenreihe: | NATO Advanced Study Institutes Series, Series C — Mathematical and Physical Sciences
70 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 © 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" |
| Beschreibung: | 1 Online-Ressource (XII, 430 p) |
| ISBN: | 9789400984899 9789400984912 |
| ISSN: | 1389-2185 |
| DOI: | 10.1007/978-94-009-8489-9 |
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| 500 | |a 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 © 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" | ||
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
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| discipline | Physik Mathematik |
| doi_str_mv | 10.1007/978-94-009-8489-9 |
| format | Electronic eBook |
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| id | DE-604.BV042415409 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:20:57Z |
| institution | BVB |
| isbn | 9789400984899 9789400984912 |
| issn | 1389-2185 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027850902 |
| oclc_num | 863780532 |
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| physical | 1 Online-Ressource (XII, 430 p) |
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| publishDate | 1981 |
| publishDateSearch | 1981 |
| publishDateSort | 1981 |
| publisher | Springer Netherlands |
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| series2 | NATO Advanced Study Institutes Series, Series C — Mathematical and Physical Sciences |
| spelling | Plaumann, Peter Verfasser aut Geometry — von Staudt’s Point of View edited by Peter Plaumann, Karl Strambach Proceedings of the NATO Advanced Study Institute, Bad Windesheim, West Germany, July 21-August 1, 1980 Dordrecht Springer Netherlands 1981 1 Online-Ressource (XII, 430 p) txt rdacontent c rdamedia cr rdacarrier NATO Advanced Study Institutes Series, Series C — Mathematical and Physical Sciences 70 1389-2185 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 © 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" Mathematics History of Mathematical Sciences Mathematik Strambach, Karl Sonstige oth https://doi.org/10.1007/978-94-009-8489-9 Verlag Volltext |
| spellingShingle | Plaumann, Peter Geometry — von Staudt’s Point of View Mathematics History of Mathematical Sciences Mathematik |
| title | Geometry — von Staudt’s Point of View |
| title_alt | Proceedings of the NATO Advanced Study Institute, Bad Windesheim, West Germany, July 21-August 1, 1980 |
| title_auth | Geometry — von Staudt’s Point of View |
| title_exact_search | Geometry — von Staudt’s Point of View |
| title_full | Geometry — von Staudt’s Point of View edited by Peter Plaumann, Karl Strambach |
| title_fullStr | Geometry — von Staudt’s Point of View edited by Peter Plaumann, Karl Strambach |
| title_full_unstemmed | Geometry — von Staudt’s Point of View edited by Peter Plaumann, Karl Strambach |
| title_short | Geometry — von Staudt’s Point of View |
| title_sort | geometry von staudt s point of view |
| topic | Mathematics History of Mathematical Sciences Mathematik |
| topic_facet | Mathematics History of Mathematical Sciences Mathematik |
| url | https://doi.org/10.1007/978-94-009-8489-9 |
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