On asymptotic commutativity degree of finite groups

Authors

  • R. Nath Tezpur University.

DOI:

https://doi.org/10.22199/issn.0717-6279-2019-04-0054

Keywords:

Finite groups, Commutativity degree

Abstract

The aim of this paper is to give a detailed account of a problema posed by P. Lescot regarding asymptotic commutativity degree of finite groups.

Author Biography

R. Nath, Tezpur University.

Dept of Mathematical Sciences.

References

A. Castelaz, "Commutativity degree of finite groups", M. A. thesis, Wake Forest University, 2010. [On line]. Available: https://bit.ly/2N9Vca7

H. Doostie and M. Maghasedi, “Certain classes of groups with commutativity degree d(G) <1/2 ”, Ars combinatoria, vol. 89, pp. 263-270, Oct. 2008.

J. Dutta, “On a problem posed by Belcastro and Sherman”, Kyungpook mathematical journal, vol. 56, no. 1, pp. 121—123, 2016. [On line]. Available: https://bit.ly/2VXyp5b

I. Erovenko and B. Sury, “Commutativity degree of wreath products of finite abelian groups”, Bulletin of the australian mathematical society, vol. 77, no. 1, pp. 31-36, Feb. 2008, doi: 10.1017/S0004972708000038

W. Gustafson, “What is the probability that two group elements commute?”, The American mathematical monthly, vol. 80, no. 9, pp. 1031-1034, Nov. 1973, doi: 10.2307/2318778.

P. Lescot, “Isoclinism classes and commutativity degrees of finite groups”, Journal of algebra, vol. 177, no. 3, pp. 847-869, Nov. 1995, doi: 10.1006/jabr.1995.1331.

P. Lescot, “Central extensions and commutativity degree”, Communication in algebra, vol. 29, no. 10, pp. 4451-4460, Mar. 2001, doi: 10.1081/AGB-100106768

R. Nath, “Commutativity degree, its generalizations, and classification of finite groups”, Ph. D. thesis, North-Eastern Hill University, 2010.

R. Nath, “Computing the commutativity degree of a class of finite groups and consequences”, Bulletin of the australian mathematical society, vol. 88, no. 3, pp. 448-452, Dec. 2013, doi: 10.1017/S0004972712001086.

D. Rusin, “What is the probability that two elements of a finite group commute?”, Pacific journal of mathematics, vol. 82, no. 1, pp. 237-247, May 1979, doi: 10.2140/pjm.1979.82.237

Published

2019-10-22

How to Cite

[1]
R. K. Nath, “On asymptotic commutativity degree of finite groups”, Proyecciones (Antofagasta, On line), vol. 38, no. 4, pp. 829-835, Oct. 2019.

Issue

Vol. 38 No. 4 (2019)

Section

Artículos
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