Skip to main content
SpringerLink
Log in

Groups that are Almost Homogeneous

  • Published:
Geometriae Dedicata Aims and scope Submit manuscript

Abstract

We classify those groups whose automorphism group has at most three orbits. In other words, we classify those groups whose holomorph is a rank 3 permutation group.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Artin, E.: Geometric Algebra, Interscience, New York, 1957.

    Google Scholar 

  2. Bourbaki, N.: Elements of Mathematics, Algebra I, Springer, Berlin, 1989.

    Google Scholar 

  3. Cronheim, A.: T-groups and their geometry, Illinois J. Math. 9(1965), 1–30.

  4. Fuchs, L.: Infinite Abelian Groups, Vol. 1, Academic Press, New York, 1970.

    Google Scholar 

  5. Gorenstein, D.: Finite Groups, Harper and Row, New York, 1968.

    Google Scholar 

  6. Greub, W. H.: Multilinear Algebra, Springer, Berlin, 1967.

    Google Scholar 

  7. Higman, G.: Suzuki 2-groups, Illinois J. Math. 7(1963), 79–96.

    Google Scholar 

  8. Higman, G., Neumann, B. H. and Neumann, H.: Embedding theorems for groups, J. London Math. Soc. 24(1949), 247–254.

    Google Scholar 

  9. Jacobson, N.: Basic Algebra I, 2nd edn, Freeman, New York, 1985.

    Google Scholar 

  10. Jungnickel, D.: Finite Fields: Structure and Arithmetics, BI-Wissenschaftsverlag, Mannheim, 1993.

    Google Scholar 

  11. Kaplansky, I.: Infinite Abelian Groups, University of Michigan Press, Ann Arbor, Michigan, 1954.

  12. Lang, S.: Algebra, Addison-Wesley, Reading, 1993.

  13. Lüneburg, H.: Die Suzukigruppen und ihre Geometrien, Lecture Notes in Math. 10, Springer, Berlin, 1965.

    Google Scholar 

  14. Murty, M. Ram: Artin's conjecture for primitive roots, Math. Intelligencer 10(4) (1988), 59–67.

    Google Scholar 

  15. Ol'shanski\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\imath}\), A. Yu.: Geometry of Defining Relations in Groups, Math. Appl. (Soviet Ser.) 70, Kluwer Academic Publ., Dordrecht, 1991

    Google Scholar 

  16. Salzmann, H., Betten, D., Grundhöfer, T., Hähl, H., Löwen, R. and Stroppel, M.: Compact Projective Planes, Expositions in Mathematics 21, De Gruyter, Berlin, 1996.

    Google Scholar 

  17. Stroppel, M.: Locally Compact Groups with Many Automorphisms, Manuscript, Stuttgart, in preparation.

  18. Stroppel, M.: Homogeneous locally compact groups, J. Algebra, to appear.

Download references

Author information

Authors and Affiliations

  1. Fachbereich Mathematik der TH, SchloΒgartenstr. 7, D-64289, Darmstadt, Germany

    Helmut Mäurer

  2. Mathematisches Institut B/1, Universität Stuttgart, Germany, D-70550, Stuttgart, Germany

    Markus Stroppel

Authors
  1. Helmut Mäurer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Markus Stroppel
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mäurer, H., Stroppel, M. Groups that are Almost Homogeneous. Geometriae Dedicata 68, 229–243 (1997). https://doi.org/10.1023/A:1005090519480

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1005090519480

Search

Navigation