Skip to main content
SpringerLink
Log in

Subgroups of Baumslag–Solitar groups

  • Published:
Algebra and Logic Aims and scope

For a graph of groups, elementary conditions are derived that are necessary and sufficient for its fundamental group to be isomorphic to a subgroup of a Baumslag–Solitar group with various simple parameters. This gives a description of all subgroups of such groups.

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. G. Baumslag and D. Solitar, “Some two-generator one-relator non-Hopfian groups,” Bull. Am. Math. Soc., 68, No. 3, 199-201 (1962).

    Article  MATH  MathSciNet  Google Scholar 

  2. J.-P. Serre, Trees, Springer, Berlin (1980).

    MATH  Google Scholar 

  3. V. A. Churkin, “Theory of groups that act on trees,” Algebra Logika, 22, No. 2, 159-165 (1983).

    Article  MATH  MathSciNet  Google Scholar 

  4. M. Clay and M. Forester, “On the isomorphism problem for generalized Baumslag–Solitar groups,” preprint, arXiv:math.GR0710.2108vl, 10 Oct. 2007.

  5. G. Levitt, “On the automorphism group of generalized Baumslag–Solitar groups,” preprint, arXiv:math.GR/0511083, 3 Nov. 2005.

  6. H. Bass, “Covering theory for graphs of groups,” J. Pure Appl. Alg., 89, Nos. 1/2, 3-47 (1993).

    Article  MATH  MathSciNet  Google Scholar 

  7. R. C. Lyndon and P. E. Schupp, Combinatorial Group Theory, Springer, Berlin (1966).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

    F. A. Dudkin

Authors
  1. F. A. Dudkin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to F. A. Dudkin.

Additional information

Supported by the Russian Ministry of Education through the Analytical Departmental Target Program (ADTP) “Development of Scientific Potential of the Higher School of Learning” (project No. 2.1.1.419).

Translated from Algebra i Logika, Vol. 48, No. 1, pp. 3-30, January–February, 2009.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dudkin, F.A. Subgroups of Baumslag–Solitar groups. Algebra Logic 48, 1–19 (2009). https://doi.org/10.1007/s10469-009-9038-0

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10469-009-9038-0

Keywords

Search

Navigation