Skip to main content
SpringerLink
Log in

Groups of Automorphisms of Tournaments

  • Published:
Order Aims and scope Submit manuscript

Abstract

By the Holland Representation Theorem, every lattice ordered group (l-group) is isomorphic to a subalgebra of the l-group of automorphisms of a chain. Since weakly associative lattice groups (wal-groups) and tournaments are non-transitive generalizations of l-groups and chains, respectively, the problem concerning the possibility of representation of wal-groups by automorphisms of tournaments arises. In the paper we describe the class of wal-groups isomorphic to wal-groups of automorphisms of tournament and show some of its properties.

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. Darnel, M. R. (1995) Theory of Lattice-Ordered Groups, Marcel Dekker, Inc., New York.

    Google Scholar 

  2. Fried, E. (1970) Tournaments and non-associative lattices, Ann. Univ. Sci. Budapest, Sect. Math. 13, 151–164.

    Google Scholar 

  3. Fried, E. (1970) A generalization of ordered algebraic systems, Acta Sci. Math. (Szeged) 13, 233–244.

    Google Scholar 

  4. Glass, A. M.W. (1981) Ordered Permutation Groups, London Math. Soc. Lecture Notes Series 55, Cambridge Univ. Press.

  5. Glass, A. M. W. (1999) Partially Ordered Groups, World Scientific, Singapore.

    Google Scholar 

  6. Glass, A. M. W. and Holland, W. C. (eds.) (1989) Lattice-Ordered Groups (Advances and Techniques), Kluwer Academic Publishers, Dordrecht.

    Google Scholar 

  7. Holland, W. C. (1963) The lattice-ordered groups of automorphisms of an ordered set, Michigan Math. J. 10, 399–408.

    Google Scholar 

  8. Kopytov, V. M. and Medvedev, N. Ya. (1994) The Theory of Lattice Ordered Groups, Kluwer Academic Publishers, Dordrecht.

    Google Scholar 

  9. Rachůnek, J. (1992) Solid subgroups of weakly associative lattice groups, Acta Univ. Palack. Olomucensis, Fac. Rer. Nat. 105, Math. 31, 13–24.

    Google Scholar 

  10. Rachůnek, J. (1996) On some varieties of weakly associative lattice groups, Czechoslovak Math. J. 46, 231–240.

    Google Scholar 

  11. Skala, H. L. (1971) Trellis theory, Algebra Universalis 1, 218–233.

    Google Scholar 

  12. Skala, H. L. (1972) Trellis Theory, Mem. Amer. Math. Soc., Providence.

Download references

Author information

Authors and Affiliations

  1. Palacký University, Tomkova 40, 779 00, Olomouc, Czech Republic

    Jiří Rachůnek

Authors
  1. Jiří Rachůnek
    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

Rachůnek, J. Groups of Automorphisms of Tournaments. Order 18, 349–357 (2001). https://doi.org/10.1023/A:1013965014631

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1013965014631

Search

Navigation