Skip to main content
Log in

On the dimensions of automorphism groups of eight-dimensional double loops

  • Published:
Monatshefte für Mathematik Aims and scope Submit manuscript

Abstract

LetD be an eight-dimensional, locally compact, connected double loop. It is proved that the dimension of the automorphism group AutD with respect to the compact-open topology is at most 16.

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.

Similar content being viewed by others

References

  1. Bödi, R.: On the embedding of zero-dimensional double loops in locally euclidean double loops. Resultate der Math.22, 657–666 (1992).

    Google Scholar 

  2. Bödi, R.: Automorphism groups of locally compact connected double loops are locally compact. Arch. Math.63, 291–294 (1993).

    Google Scholar 

  3. Bödi, R.: On the dimensions of automorphism groups of 4-dimensional double loops. (to appear in Math. Z.).

  4. Borel, A.: Seminar on transformation groups. Ann. of Math. Stud.46, Princeton: Univ. Press. 1960.

    Google Scholar 

  5. Bredon, G. E.: Sheaf Theory. New York: McGraw-Hill. 1967.

    Google Scholar 

  6. Cartan, H., Eilenberg, S.: Homological Algebra. Princeton: Univ. Press. 1956.

    Google Scholar 

  7. Dold, A.: Lectures on Algebraic Topology. Berlin-Heidelberg-New York: Springer. 1972.

    Google Scholar 

  8. Freudenthal, H., de Vries, H.: Linear Lie Groups. New York-London: Academic Press. 1969.

    Google Scholar 

  9. Grundhöfer, T., Salzmann, H.: Locally compact double loops and ternary fields. In: Chein, O., Pflugfelder, H. D., Smith, J. D. H. (eds.) Quasigroups and Loops: Theory and Applications. pp. 313–356. Berlin: Heldermann. 1990.

    Google Scholar 

  10. Halder, H. R.: Dimension der Bahn lokal kompakter Gruppen. Arch. Math.22, 302–303 (1971).

    Google Scholar 

  11. Hewitt, E., Ross, K. A.: Abstract Harmonic Analysis I, 2nd edn. Berlin-Heidelberg-New York: Springer. 1979.

    Google Scholar 

  12. Iwasawa, K.: On some types of topological groups. Ann. of Math.50, 507–558 (1949).

    Google Scholar 

  13. Kodama, Y.: A necessary and sufficient condition under which dimX×Y=dimX+dimY. Proc. Japan Acad.36, 400–404 (1960).

    Google Scholar 

  14. Löwen, R.: Topology and dimension of stable planes: On a conjecture of H. Freudenthal. J. Reine Angew. Math.343, 108–122 (1983).

    Google Scholar 

  15. Massey, W. S.: Singular Homology Theory. Berlin-Heidelberg-New York: Springer. 1980.

    Google Scholar 

  16. Montgomery, D., Zippin, L.: Topological Transformation Groups. New York: Wiley. 1955.

    Google Scholar 

  17. Mostow, G. D.: The extensibility of local Lie groups of transformations. Ann. of Math.52, 606–636 (1950).

    Google Scholar 

  18. Nagami, K.: Dimension-theoretical structure of locally compact groups. J. Math. Soc. Japan14, 379–396 (1962).

    Google Scholar 

  19. Pears, A. R.: Dimension theory of general spaces. Cambridge: University Press. 1975.

    Google Scholar 

  20. Salzmann, H.: Topological planes. Adv. Math.2, 1–60 (1967).

    Google Scholar 

  21. Salzmann, H.: Automorphismengruppen achtdimensionaler Ternärkörper. Math. Z.166, 265–275 (1979).

    Google Scholar 

  22. Salzmann, H.: Compact 8-dimensional projective planes with large collineation groups. Geom. Dedicata8, 139–161 (1979).

    Google Scholar 

  23. Smith, P. A.: New results and old problems in finite transformation groups. Bull. Amer. Math. Soc.66, 401–415 (1960).

    Google Scholar 

  24. Spanier, E. H.: Algebraic Topology. New York: McGraw-Hill. 1966.

    Google Scholar 

  25. Völklein, H.: Transitivitätsfragen bei linearen Liegruppen. Arch. Math.36, 23–34 (1981).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bödi, R. On the dimensions of automorphism groups of eight-dimensional double loops. Monatshefte für Mathematik 117, 1–16 (1994). https://doi.org/10.1007/BF01299308

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01299308

Keywords

Navigation