Skip to main content
Log in

k-transitive permutation groups andk-planes

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Arens, R.: Topologies for homeomorphism groups. Amer. J. Math.68, 593–610 (1946)

    Google Scholar 

  2. Barlotti, A.: Sul gruppo delle proiettività di una retta in sè nei piani liberi e nei piani aperti. Rend. Sem. Mat. Univ. Padova34, 135–159 (1964)

    Google Scholar 

  3. Barlotti, A., Schreiber, E., Strambach, K.: The group of projectivities in free-like geometries. Rend. Sem. Mat. Univ. Padova60, 183–200 (1978)

    Google Scholar 

  4. Barlotti, A., Strambach, K.: The geometry of binary systems. Advances in Mathematics49, 1–105 (1983)

    Google Scholar 

  5. Benz, W.: Permutations and plane sections of a ruled quadric. Symposia Mathematica5, 325–339 (1970)

    Google Scholar 

  6. Benz, W.: Vorlesungen über Geometrie der Algebren. Berlin-Heidelberg-New York: Springer 1973

    Google Scholar 

  7. Cameron, P.J.: Finite permutation groups and finite simple groups. Bull. London Math. Soc.13, 1–22 (1981)

    Google Scholar 

  8. Cameron, P.J.: Orbits, enumeration and colouring. In: Combinatorial Mathematics IX, Proc. Brisbane, Australia 1981. Lecture Notes in Math.952, pp. 34–66. Berlin-Heidelberg-New York: Springer 1982

    Google Scholar 

  9. Dugundji, J.: Topology. Boston, Mass.: Allyn and Bacon 1966

    Google Scholar 

  10. Freudenthal, H.: Über die Enden topologischer Räume und Gruppen. Math. Z.33, 692–713 (1931)

    Google Scholar 

  11. Funk, M., Kegel, O.H., Strambach, K.: Gruppenuniversalität und Homogenisierbarkeit. To appear

  12. Gleason, A.M., Palais, R.S.: On a class of transformation groups. Amer. J. Math.79, 631–648 (1957)

    Google Scholar 

  13. Hall, M. Jr.: Projective planes. Trans. Amer. Math. Soc.54, 229–277 (1943)

    Google Scholar 

  14. Hall, M., Jr.: The Theory of Groups. New York: Macmillan Co. 1959

    Google Scholar 

  15. Heise, W.: On sharplyk-ply transitive sets of permutations. J. Geometry6, 185 (1975)

    Google Scholar 

  16. Heise, W., Karzel, H.: Symmetrische Minkowski Ebenen. J. Geometry3, 5–20 (1973)

    Google Scholar 

  17. Heise, W., Sörensen, K.: Freie Minkowski-Ebenenerweiterungen. J. Geometry3, 1–4 (1973)

    Google Scholar 

  18. Heise, W., Sörensen, K.: Scharfn-fach transitive Permutationsmengen. Abh. Math. Sem. Univ. Hamburg43, 144–145 (1975)

    Google Scholar 

  19. Karzel, H.: Zusammenhänge zwischen Fastbereichen, scharf zweifach transitiven Permutationsgruppen und 2-Strukturen mit Rechtecksaxiom. Abh. Math. Sem. Univ. Hamburg32, 191–206 (1968)

    Google Scholar 

  20. Karzel, H., Kroll, H.J.: Perspectivities in Circle Geometries. In: Geometry-von Staudt's point of view (P. Plaumann and K. Strambach, eds.), pp. 51–99. Dordrecht-Boston: Reidel 1980

    Google Scholar 

  21. Kegel, O.H.: Examples of highly transitive permutation groups. Rend. Sem. Mat. Univ. Padova63, 297–300 (1980)

    Google Scholar 

  22. Kegel, O.H., Schleiermacher, A.: Amalgams and embeddings of projective planes. Geom. Dedicata2, 379–395 (1973)

    Google Scholar 

  23. Kerby, W.: On infinite sharply multiply transitive groups. Hamburger Math. Einzelschriften6. Göttingen: Vandenhoeck and Ruprecht 1974

    Google Scholar 

  24. Knop, F.: Mehrfach transitive Operationen algebraischer Gruppen. Arch. Math. (Basel)41, 438–446 (1983)

    Google Scholar 

  25. Kurzweil, H.: Endliche Gruppen, Hochschultexte. Berlin-Heidelberg-New York: Springer 1977

    Google Scholar 

  26. Lorimer, P.: A property of the groupsPΓL(m,q), q≧5. Proc. Amer. Mat. Soc.37, 393–396 (1973)

    Google Scholar 

  27. Lorimer, P.: Finite projective planes and sharply 2-transitive subsets of finite groups. Proc. of the second Intern. Conference on the Theory of Groups (Canberra 1973) Lecture Notes in Math.372, pp. 432–436. Berlin-Heidelberg-New York: Springer 1974

    Google Scholar 

  28. Löwen, R.: Projectivities and the geometric structure of topological planes. In: Geometry-von Staudt's point of view (P. Plaumann and K. Strambach, eds.), pp. 339–372. Dordrecht-Boston: Reidel 1980

    Google Scholar 

  29. Matsumura, H., Oort, F.: Representability of group functors and automorphisms of algebraic schemes. Invent. Math.4, 1–25 (1967)

    Google Scholar 

  30. McDonough, T.P.: A Permutation representation of a free group. Quart. J. Math. Oxford Ser. (2)28, 353–356 (1977)

    Google Scholar 

  31. Meschiari, M., Quattrocchi, P.: Una classificazione delle strutture di incidenza associate ad insiemi di sostituzioni strettamente 3-transitivi finiti. Atti Sem. Mat. Fis. Univ. Modena24, 123–141 (1975)

    Google Scholar 

  32. Pedrini, C.: 3-reti (non immergibili) aventi dei piani duali di quelli di Moulton quali sottopiani. Rend. Accad. Naz. Lincei40, 385–392 (1966)

    Google Scholar 

  33. Quattrocchi, P.: Sugli insiemi di sostituzioni strettamente 3-transitivi finiti. Atti Sem. Mat. Fis. Univ. Modena24, 279–288 (1975)

    Google Scholar 

  34. Rosati, L.A.: Sugli insiemi di sostituzioni strettamente 3-transitivi. Atti Convegni Lincei17 (Coll. Intern. Teorie Combinatorie Roma 3–15 settembre 1973), Tomo 2. Rome: Accad. Naz. Lincei 1976

    Google Scholar 

  35. Scheerer, H.: Restklassenräume kompakter zusammenhängender Gruppen mit Schnitt. Math. Ann.206, 144–155 (1973)

    Google Scholar 

  36. Shult, E.E.: Permutation groups with few fixed points. In Geometry-von Staudt's point of view (P. Plaumann and K. Strambach, eds.), pp. 275–311. Dordrecht-Boston: Reidel 1981

    Google Scholar 

  37. Strambach, K.: Rechtsdistributive Quasigruppen auf 1-Mannigfaltigkeiten. Math. Z.145, 63–68 (1975)

    Google Scholar 

  38. Szenthe, J.: On the topological characterization of transitive Lie groups actions. Acta Sci. Math. Szeged 36, 323–344 (1974)

    Google Scholar 

  39. Tits, J.: Sur certaines classes d'espaces homogènes de groupes de Lie. Acad. Roy. Belg. Cl. Sci. Mem. Collect 8°,29, No. 3 (1955)

    Google Scholar 

  40. Wefelscheid, H.: Zur Planarität vonKT-Fastkörpern. Arch. Math. (Basel)36, 302–304 (1981)

    Google Scholar 

  41. Whyburn, G.T.: Analytic Topology. Providence: Amer. Math. Soc. 1942

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

The authors wish to acknowledge with sincere thanks the support given by the “Istituto di Analisi Globale e Applicazioni” of the C.N.R.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Barlotti, A., Strambach, K. k-transitive permutation groups andk-planes. Math Z 185, 465–485 (1984). https://doi.org/10.1007/BF01236257

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01236257

Keywords

Navigation