Skip to main content
SpringerLink
Log in

The free spectrum of the variety of bands

  • Short note
  • Published:
Semigroup Forum Aims and scope Submit manuscript

Abstract

In this short note we give an asymptotic formula for the p n sequence of the variety of bands, namely, \(p_{n}(\mathcal{B})=\frac{1}{n^{2}}K^{2^{n+1}}(1+O(\frac{1}{n})),\) for some constant K. This yields a formula for the free spectrum of this variety.

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. Crvenković, S., Ruškuc, N.: Log-linear varieties of semigroups. Algebra Universalis 33, 370–374 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  2. Crvenković, S., Dolinka, I., Ruškuc, N.: Finite semigroups with few term operations. J. Pure Appl. Algebra 157, 205–214 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  3. Crvenković, S., Dolinka, I., Ruškuc, N.: The Berman conjecture is true for finite surjective semigroups and their inflations. Semigroup Forum 62, 103–114 (2001)

    MathSciNet  MATH  Google Scholar 

  4. Green, J.A., Rees, D.: On semigroups in which x r=x. Proc. Camb. Philos. Soc. 48, 35–40 (1952)

    Article  MATH  MathSciNet  Google Scholar 

  5. Higman, G.: The orders of relatively free groups. In: Kovács, L.G., Neumann, B.H. (eds.) Proc. Internat. Conf. Theory of Groups, Austral. Nat. Univ. 1965, pp. 153–165. Gordon and Breach, New York (1967)

    Google Scholar 

  6. Kátai, K., Szabó, C.: The free spectra of the variety generated by the completely 0-simple semigroups. Glasgow J. Math. (to appear)

  7. Kátai, K., Szabó, C.: The free spectra of exact varieties. Manuscript (2006)

  8. Neumann, P.: Some indecomposable varieties of groups. Q. J. Math. Oxford 14, 46–50 (1963)

    Article  MATH  Google Scholar 

  9. Pluhár, G., Wood, J.: The free spectra of varieties generated by idempotent semigroups. Algebra Discrete Math. (to appear)

Download references

Author information

Authors and Affiliations

  1. Department of Algebra and Number Theory, Eötvös Loránd University, 1117, Budapest, Pázmány Péter sétány 1/c, Hungary

    Gabriella Pluhár & Csaba Szabó

Authors
  1. Gabriella Pluhár
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Csaba Szabó
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Csaba Szabó.

Additional information

Communicated by László Márki

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pluhár, G., Szabó, C. The free spectrum of the variety of bands. Semigroup Forum 76, 576–578 (2008). https://doi.org/10.1007/s00233-007-9021-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00233-007-9021-9

Keywords

Search

Navigation