Skip to main content
SpringerLink
Log in

Lower Central Series of Baumslag–Solitar Groups

  • Published:
Algebra and Logic Aims and scope

We look at Baumslag–Solitar groups. Lower central series are given for residually nilpotent Baumslag–Solitar groups. For some Baumslag–Solitar groups that are not residually nilpotent, we find the intersection of all terms of the lower central series. Also we point out non-Abelian Baumslag–Solitar groups having lower central series of length 2. For some Baumslag–Solitar groups, a connection is found between an intersection of subgroups of finite index and an intersection of terms of the lower central series.

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  MathSciNet  Google Scholar 

  2. D. Moldavanskii, “On some residual properties of Baumslag–Solitar groups,” 2013; https://arxiv.org/abs/1310.3585.

    MATH  Google Scholar 

  3. D. Moldavanskii, “On the residual properties of Baumslag–Solitar groups,” Commun. Alg., 46, No. 9, 3766-3778 (2018).

    Article  MathSciNet  Google Scholar 

  4. D. I. Moldavanskii, “Residual nilpotence of groups with one defining relation,” Mat. Zametki, 107, No. 5, 752-759 (2020).

    Article  MathSciNet  Google Scholar 

  5. A. I. Mal’tsev, “Homomorphisms onto finite groups,” Uch. Zap. Ivanovo Ped. Inst., 18, No. 5, 49-60 (1958).

    Google Scholar 

  6. S. Meskin, “Nonresidually finite one-relator groups,” Trans. Am. Math. Soc., 164, 105-114 (1972).

    Article  MathSciNet  Google Scholar 

  7. D. I. Moldavanskii, “p-Finite residuality of HNN-extensions,” Vestnik Ivanovo St. Univ., Biol., Khim., Fiz., Mat., Iss. 3, 129-140 (2000).

  8. V. G. Bardakov, “On a width of verbal subgroups of certain free constructions,” Algebra and Logic, 36, No. 5, 288-301 (1997).

    Article  MathSciNet  Google Scholar 

  9. D. I. Moldavanskii, “The intersection of the subgroups of finite index in Baumslag–Solitar groups,” Mat. Zametki, 87, No. 1, 92-100 (2010).

    Article  MathSciNet  Google Scholar 

  10. M. Forester, “Splittings of generalized Baumslag–Solitar groups,” Geom. Dedicata, 121, No. 1, 43-59 (2006).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics. Novosibirsk State University. Novosibirsk State Agrarian University, Novosibirsk. Tomsk State University, Tomsk, Russia

    V. G. Bardakov

  2. Sobolev Institute of Mathematics. Novosibirsk State University, Novosibirsk. Tomsk State University, Tomsk, Russia

    M. V. Neshchadim

Authors
  1. V. G. Bardakov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. V. Neshchadim
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. G. Bardakov.

Additional information

Translated from Algebra i Logika, Vol. 59, No. 4, pp. 413-431, July-August, 2020. Russian https://doi.org/10.33048/alglog.2020.59.401.

M. V. Neshchadim is Supported by RFBR, project No. 19-01-00569.

V. G. Bardakov is Supported by RFBR, project No. 18-01-00057.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bardakov, V.G., Neshchadim, M.V. Lower Central Series of Baumslag–Solitar Groups. Algebra Logic 59, 281–294 (2020). https://doi.org/10.1007/s10469-020-09601-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10469-020-09601-z

Keywords

Search

Navigation