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Locally Compact Hughes Planes

Published online by Cambridge University Press:  20 November 2018

Markus Stroppel
Markus Stroppel*
Affiliation:
Fachbereich Mathematik Technische Hochschule Darmstadt Schloβgartenstr. 7 D-64289 Darmstadt Germany e-mail:[email protected]
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Abstract

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Among the eight-dimensional stable planes, the compact connected generalized Hughes planes and the geometries induced on the outer points are characterized by the property that these planes admit an effective action of the group SL3 ℂ.

Keywords

51H1051H2051A35
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 1 , 01 March 1994 , pp. 112 - 123
Copyright
Copyright © Canadian Mathematical Society 1994

References

1. Arens, R., Topologies for homeomorphism groups, Amer. J. Math. 68(1946), 593–610.Google Scholar
2. Biliotti, M., Su una generalizzazione cli Dembowski deipiani di Hughes, Boll. Un. Mat. Ital. B (5) 16( 1979), 674–693.Google Scholar
3. Bourbaki, N., Groupes et algèbres de Lie, Chapter I, Hermann, Paris, 1971.Google Scholar
4. Cartan, H. and Eilenberg, S., Homological algebra, Princeton Univ. Press, 1956.Google Scholar
5. Dembowski, P., Generalized Hughes planes, Canad. J. Math. 23( 1971 ), 481–494.Google Scholar
6. Dugundji, J., Topology, Allyn & Bacon, Boston, 1966.Google Scholar
7. Hughes, D. R., A class of non-desarguesianprojective planes, Canad. J. Math. 9(1957), 378–388.Google Scholar
8. Kalscheuer, F., Die Bestimmung aller stetigen Fastkörper ¨berdem Körperder reellen Zahlen als Grundkörper, Abh. Math. Sem. Univ. Hamburg, 13(1940), 413–435.Google Scholar
9. Knarr, N. and Weigand, C., Ein Kriterium f¨r topologische Ternärkörper, Arch. Math. 46(1986), 368–370.Google Scholar
10. Löwen, R., Vierdimensionale stabile Ebenen, Geom. Dedicata 5(1976), 239–294.Google Scholar
11. Löwen, R., Topology and dimension of stable planes: On a conjecture by H. Freudenthal, J. Reine Angew. Math. 343(1983), 108–122.Google Scholar
12. Löwen, R., Actions of SO (3) on ^-dimensional stable planes, Aequationes Math. 30(1986), 212–222.Google Scholar
13. Mann, L. N., Dimensions of compact transformation groups, Michigan Math. J. 14(1967),433–444.Google Scholar
14. Richardson, R., Groups acting on the 4-sphere, Illinois J. Math. 5(1961), 474–485.Google Scholar
15. Salzmann, H., Kompakte, %-dimensionale projektive Ebenen mit grofier Kollineationsgruppe, Math. Z. 176(1981),345–357.Google Scholar
16. Smith, P. A., New results and old problems infinite transformation groups, Bull. Amer. Math. Soc. 66(1960), 401–415.Google Scholar
17. Stroppel, M., Achtdimensionale stabile Ebenen mit quasieinfacher Automorphismengruppe, Dissertation, Tubingen, 1991.Google Scholar
18. Stroppel, M., Reconstruction of incidence geometries from groups of automorphisms, Arch. Math. 58(1992), 621–624.Google Scholar
19. Stroppel, M., Planar groups of automorphisms of stable planes, J. Geom. 44(1992), 184–200.Google Scholar
20. Stroppel, M., Quasiperspectivities in stable planes, Monatsh. Math. 115(1993), 183–189.Google Scholar
21. Stroppel, M., Compact groups of automorphisms of stable planes, Forum Math. (1993), to appear.Google Scholar
22. Tits, J., Sur les groupes doublement transitifs continus: correction et compléments, Comm. Math. Helv. 30(1956), 234–240.Google Scholar