Skip to main content
SpringerLink
Log in

Is supernilpotence super nilpotence?

  • Published:
Algebra universalis Aims and scope Submit manuscript

Abstract

We show that the answer to the question in the title is: “Yes, for finite algebras”.

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. Aichinger, E., Mudrinski, N.: Some applications of higher commutators in Mal’cev algebras. Algebra Univ. 63(4), 367–403 (2010)

    Article  MathSciNet  Google Scholar 

  2. Bruck, R.H.: Contributions to the theory of loops. Trans. Am. Math. Soc. 60, 245–354 (1946)

    Article  MathSciNet  Google Scholar 

  3. Capelli, A.: Sopra la composizione dei gruppi di sostituzioni. Mem. R. Accad. Lincei 19, 262–272 (1884)

    MATH  Google Scholar 

  4. Hobby, D., McKenzie, R.: The Structure of Finite Algebras, Contemporary Mathematics, vol. 76. American Mathematical Society, Providence (1988)

    Book  Google Scholar 

  5. Kearnes, K.A.: An order-theoretic property of the commutator. Int. J. Algebra Comput. 3(4), 491–533 (1993)

    Article  MathSciNet  Google Scholar 

  6. Kearnes, K.A.: A Hamiltonian property for nilpotent algebras. Algebra Univ. 37(4), 403–421 (1997)

    Article  MathSciNet  Google Scholar 

  7. Kearnes, K.A.: Congruence modular varieties with small free spectra. Algebra Univ. 42(3), 165–181 (1999)

    Article  MathSciNet  Google Scholar 

  8. Kearnes, K.A., Kiss, E.W.: Finite algebras of finite complexity. Discret. Math. 207(1–3), 89–135 (1999)

    Article  MathSciNet  Google Scholar 

  9. Kearnes, K.A., Kiss, E.W.: Residual smallness and weak centrality. Int. J. Algebra Comput. 13, 35–59 (2003)

    Article  MathSciNet  Google Scholar 

  10. Moore, M., Moorhead, A.: Supernilpotence need not imply nilpotence. J. Algebra 535, 225–250 (2019)

    Article  MathSciNet  Google Scholar 

  11. Moorhead, A.: Higher commutator theory for congruence modular varieties. J. Algebra 513, 133–158 (2018)

    Article  MathSciNet  Google Scholar 

  12. Peirce, B.: Linear associative algebra. Am. J. Math. 4(1–4), 97–229 (1881)

    Article  MathSciNet  Google Scholar 

  13. Weinell, S.: On the Descending Central Series of Higher Commutators for Simple Algebras. Ph.D. Thesis, University of Colorado at Boulder (2019)

  14. Wright, C.R.B.: On the multiplication group of a loop. Ill. J. Math. 13, 660–673 (1969)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Colorado, Boulder, CO,  80309-0395, USA

    Keith A. Kearnes & Ágnes Szendrei

Authors
  1. Keith A. Kearnes
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ágnes Szendrei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Keith A. Kearnes.

Additional information

Dedicated to Ralph Freese, Bill Lampe, and J. B. Nation.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This article is part of the topical collection “Algebras and Lattices in Hawaii” edited by W. DeMeo.

This material is based upon work supported by the National Science Foundation Grant no. DMS 1500254, the Hungarian National Foundation for Scientific Research (OTKA) Grant no. K115518, and the National Research, Development and Innovation Fund of Hungary (NKFI) Grant no. K128042.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kearnes, K.A., Szendrei, Á. Is supernilpotence super nilpotence?. Algebra Univers. 81, 3 (2020). https://doi.org/10.1007/s00012-019-0632-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00012-019-0632-2

Keywords

Mathematics Subject Classification

Search

Navigation