Skip to main content

Permutation Groups Whose Subgroups Have Just Finitely Many Orbits

  • Chapter
Ordered Groups and Infinite Permutation Groups

Part of the book series: Mathematics and Its Applications ((MAIA,volume 354))

Abstract

In this note we answer a question of Peter Neumann, based on some earlier more general questions of R. Zimmer concerning actions of arithmetic groups and Lie groups on manifolds. The main question of Zimmer is the following.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. P. J. Cameron, Oligomorphic Permutation Groups, London Math. Soc. Lecture Notes Series 152, Cambridge University Press, Cambridge, 1990.

    Google Scholar 

  2. Gy. Károlyi, S. J. Kovács, P. P. Pálfy, Doubly transitive permutation groups with abelian stabiliser, Aequationes Math. 39 (1990), 161–166.

    Article  MathSciNet  MATH  Google Scholar 

  3. H. D. Macpherson and C. E. Praeger, Cycle types in infinite permutation groups, J. Algebra, to appear.

    Google Scholar 

  4. V. D. Mazurov, Doubly transitive permutation groups, Sibirsk. Mat. Zh. 31 (1990), 102 – 104 (in Russian).

    MathSciNet  Google Scholar 

  5. P. M. Neumann, Automorphisms of the rational world, J. London Math. Soc. 32 (1985), 439–448.

    Article  MathSciNet  MATH  Google Scholar 

  6. W.R. Scott, Group Theory, Prentice-Hall, Englewood Cliffs, 1964.

    MATH  Google Scholar 

  7. J. K. Truss, The group of the countable universal graph, Math. Proc. Cam-bridge Philos. Soc. 98 (1985), 213–245.

    Article  MathSciNet  MATH  Google Scholar 

  8. J. K. Truss, The group of almost automorphisms of the countable universal graph, Math. Proc. Cambridge Philos. Soc. 105 (1989), 223–236.

    Article  MathSciNet  MATH  Google Scholar 

  9. J. K. Truss, Generic automorphisms of homogeneous structures, Proc. London Math. Soc., to appear.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Kluwer Academic Publishers

About this chapter

Cite this chapter

Macpherson, D. (1996). Permutation Groups Whose Subgroups Have Just Finitely Many Orbits. In: Holland, W.C. (eds) Ordered Groups and Infinite Permutation Groups. Mathematics and Its Applications, vol 354. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3443-9_8

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-3443-9_8

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-3445-3

  • Online ISBN: 978-1-4613-3443-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics