Skip to main content
SpringerLink
Log in

On a lower bound of commutativity degree

  • Published:
Rendiconti del Circolo Matematico di Palermo Aims and scope Submit manuscript

Abstract

The commutativity degree of a finite group G, denoted by Pr(G), is the probability that a randomly chosen pair of elements of G commute. The object of this paper is to derive a lower bound for Pr(G) and study some of its consequences towards characterizing G.

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. Espuelas, A.: On certain groups of central type, Proc. Amer. Math. Soc., 97 (1986), (1), 16–18

    Article  MATH  MathSciNet  Google Scholar 

  2. Gustafson, W.H.: What is the probability that two group elements commute?, Amer. Math. Monthly 80 (1973), 1031–1034

    Article  MATH  MathSciNet  Google Scholar 

  3. Guralnick, R.M., Robinson, G. R.: On the commuting probability in finite groups, J. Algebra 300 (2006), (2), 509–528

    Article  MATH  MathSciNet  Google Scholar 

  4. Hall, P.: The classification of prime power groups, J. Reine Angew. Math. 182 (1940), 130–141

    MathSciNet  Google Scholar 

  5. Isaacs, I.M.: Character theory of finite groups. New York: Dover Publications, Inc. (1994)

    MATH  Google Scholar 

  6. Joseph, K.S.: Commutativity in non-abelian groups. (Unpublished Ph. D. thesis) Los Angeles: University of California (1969)

    Google Scholar 

  7. Kappe, L., Morse, R.F.: On commutators in groups (English summary) Groups St. Andrews 2005. Vol. 2, 531–558, (London Math. Soc. Lecture Note Ser. 340) Cambridge: Cambridge Univ. Press (2007)

    Google Scholar 

  8. Moghaddam, M.R.R., Salemkar, A. R., Chiti, K.: n-Isoclinism classes and n-nilpotency degree of finite groups, Algebra Colloq. 12 (2005), (2), 225–261

    MathSciNet  Google Scholar 

  9. Pournaki, M. R., Sobhani, R.: Probability that the commutator of two group elements is equal to a given element, J. Pure Appl. Algebra 212 (2008), 727–734

    Article  MATH  MathSciNet  Google Scholar 

  10. Robinson, D.J.S.: A course in the theory of groups (second edition). (Graduate Text in Mathematics 80) New York: Springer (1996)

    Google Scholar 

  11. Rotman, J.J.: An introduction to the theory of groups (third edition). Allyn and Bacon, Inc. (1984)

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, North-Eastern Hill University, Permanent Campus, Shillong, 793022, Meghalaya, India

    Rajat Kanti Nath & Ashish Kumar Das

Authors
  1. Rajat Kanti Nath
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ashish Kumar Das
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rajat Kanti Nath.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nath, R.K., Das, A.K. On a lower bound of commutativity degree. Rend. Circ. Mat. Palermo 59, 137–142 (2010). https://doi.org/10.1007/s12215-010-0010-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12215-010-0010-6

Keywords

Mathematics Subject Classification (2000)

Search

Navigation