Journal of Mathematical Sciences

, Volume 166, Issue 6, pp 806–812 | Cite as

On semidirect products and wreath products of partially ordered groups

Article
First Online:
  • 22 Downloads

Abstract

The notions of Cartesian and semidirect products for partially ordered groups are considered. A series of results on those products of \( \mathcal{A}\mathcal{O} \)-groups and interpolation groups is obtained. Some results concerning wreath products of directed groups are obtained.

Keywords

Positive Integer Normal Subgroup Semidirect Product Orthogonality Condition Wreath Product 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    L. Fuchs, Partially Ordered Algebraic Systems, Pergamon Press, Oxford (1963).MATHGoogle Scholar
  2. 2.
    M. I. Kargapolov and Ju. I. Merzljakov, Fundamentals of the Theory of Groups, Springer, Berlin (1979).MATHGoogle Scholar
  3. 3.
    V. M. Kopytov, Lattice-Ordered Groups [in Russian], Nauka, Moscow (1984).MATHGoogle Scholar
  4. 4.
    V. M. Kopytov and N. Ja. Medvedev, Right-Ordered Groups [in Russian], Nauchnaja Kniga, Novosibirsk (1996).Google Scholar
  5. 5.
    E. E. Shirshova, “On Archimedean extensions of AO-groups,” J. Math. Sci., 102, No. 6, 4662–4666 (2000).MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    E. E. Shirshova, “On groups with the almost orthogonality condition,” Commun. Algebra, 28, No. 10, 4803–4818 (2000).MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    E. E. Shirshova, “On homomorphisms of AO-groups,” in: Universal Algebra and Its Applications. Int. Sem. Proc. [in Russian], Peremena, Volgograd (2000), pp. 287–294.Google Scholar
  8. 8.
    E. E. Shirshova, “On a generalization of the notion of orthogonality and on the Riesz groups,” Math. Notes, 69, No. 1, 107–115 (2001).MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    E. E. Shirshova, “On Cartesian products of AO-groups,” in: Int. Algebraic Conf. Abstracts [in Russian], Moscow (2008), pp. 257–258.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  1. 1.Moscow Pedagogical State UniversityMoscowRussia

Personalised recommendations