Skip to main content
SpringerLink
Log in

The structure of transitive ordered permutation groups

  • Published:
Czechoslovak Mathematical Journal Aims and scope Submit manuscript

Abstract

We give some necessary and sufficient conditions for transitive l-permutation groups to be 2-transitive. We also discuss primitive components and give necessary and sufficient conditions for transitive l-permutation groups to be normal-valued.

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. W. C. Holland: Transitive lattice-ordered permutation groups. Math. Zeit. 87 (1965), 420–433; MR31 (1966), #2310.

    Google Scholar 

  2. A. M. W. Glass: Ordered Permutation Groups. Cambridge University Press, 1981, pp. 76–116.

  3. Z. T. Zhu and J. M. Huang: Stability of l-permutation groups. J. of Nanjing Uni. Math. Biquarterly 11, No. 1 (1994), 18–21.

    Google Scholar 

  4. M. Anderson and T. Feil: Lattice-Ordered Groups. D. Reidel Publishing Company, Dordrecht, Holland, 1988, pp. 29–31.

    Google Scholar 

  5. Z. T. Zhu and J. M. Huang: Congruent pairs on a set. Chinese Quarterly Journal of Math. 9, No. 3 (1994), 37–41.

    Google Scholar 

  6. S. H. McClearly: The structure of intransitive ordered permutation groups. Algebra Universalis 6 (1976), 229–255.

    Google Scholar 

  7. A. M. W. Glass: Elementary types of automorphisms of linearly ordered sets-a survey. Algebra, Carbondale 1980 (R. K. Amayo, ed. ). Springer, Lecture Notes No. 848, pp. 218–229.

  8. S. H. McClearly. The structure of ordered permutation groups applied to lattice-ordered groups. Notices Amer. Math. Soc., 21 (1974), February, # 712–714, PA336.

  9. Z. T. Zhu and Q. Chen: The universal mapping problems of the l-group category. Chinese Journal of Math. 23, No. 2 (1995), 131–140.

    Google Scholar 

  10. A.. M. W. Glass and W. C. Holland (Eds): Lattice-Ordered Groups. Kluwer Academic Publishers, 1989, pp. 23–40.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Nanjing Normal University, Nanjing, 210097, People's Republic of China

    Zhu Zuo-Tong

  2. Department of Mathematics, Nanjing University, Nanjing, 210093, People's Republic of China

    Huang Zhenyu

Authors
  1. Zhu Zuo-Tong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Huang Zhenyu
    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

Zuo-Tong, Z., Zhenyu, H. The structure of transitive ordered permutation groups. Czechoslovak Mathematical Journal 49, 811–815 (1999). https://doi.org/10.1023/A:1022405201916

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1022405201916

Search

Navigation