Skip to main content
SpringerLink
Log in

Invariable generation of iterated wreath products of cyclic groups

  • Original Paper
  • Published:
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry Aims and scope Submit manuscript

Abstract

Given a sequence \(\{C_i\}_{i \in \mathbb N}\) of cyclic groups of prime orders, let \(\Gamma _\infty \) be the inverse limit of the iterated wreath products \(C_m \wr \cdots \wr C_2 \wr C_1\). We prove that the profinite group \(\Gamma _\infty \) is not topologically finitely invariably generated.

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

  • Bondarenko, I.: Finite generation of iterated wreath products. Arch. Math. (Basel) 95(4), 301–308 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  • Detomi, E., Lucchini, A.: Characterization of finitely generated infinitely iterated wreath products. Forum Math. 25(4), 867–886 (2013)

    MathSciNet  MATH  Google Scholar 

  • Detomi, E., Lucchini, A.: Invariable generation with elements of coprime prime-power orders. J. Algebra 423, 683–701 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  • Detomi, E., Lucchini, A.: Invariable generation of prosoluble groups. Israel J. Math. 211(1), 481–491 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  • Dixon, J.D.: Random sets which invariably generate the symmetric group. Discrete Math. 105, 25–39 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  • Kantor, W.M., Lubotzky, A., Shalev, A.: Invariable generation and the Chebotarev invariant of a finite group. J. Algebra 348, 302–314 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  • Kantor, W.M., Lubotzky, A., Shalev, A.: Invariable generation of infinite group. J. Algebra 421, 296310 (2015)

    MathSciNet  MATH  Google Scholar 

  • Lucchini, A.: Generating wreath products. Arch. Math. (Basel) 62(6), 481–490 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  • Stammbach, U.: Cohomological characterisations of finite solvable and nilpotent groups. J. Pure Appl. Algebra 11(1–3), 293–301 (1977/1978)

  • Wiegold, J.: Transitive groups with fixed-point-free permutations. Arch. Math. (Basel) 27, 473–475 (1976)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica “Tullio Levi-Civita”, Università degli Studi di Padova, Via Trieste 63, 35121, Padua, Italy

    Andrea Lucchini

Authors
  1. Andrea Lucchini
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Andrea Lucchini.

Additional information

Partially supported by Università di Padova (Progetto di Ricerca di Ateneo: “Invariable generation of groups”).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lucchini, A. Invariable generation of iterated wreath products of cyclic groups. Beitr Algebra Geom 58, 477–482 (2017). https://doi.org/10.1007/s13366-016-0326-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13366-016-0326-2

Keywords

Mathematics Subject Classification

Search

Navigation