Research Article | OPEN ACCESS
Finite Groups with the Same Commuting Probability
1K. Moradipour, 1N.H. Sarmin and 2A. Erfanian
1Department of Mathematical Science, Faculty of Science and Ibnu Sina Institute for Fundamental Science Studies, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
2Department of Pure Mathematics, Faculty of Mathematical Sciences, Ferdowsi
University of Mashhad, Mashhad, Iran
Research Journal of Applied Sciences, Engineering and Technology 2013 13:3525-3528
Received: June 19, 2012 | Accepted: July 04, 2012 | Published: April 15, 2013
Abstract
Let G be a finite group. The commutativity degree of G, denoted by Pr(G), is the probability that a randomly selected pairs of elements of the group commute. In this study we give an explicit formula for the number of conjugacy classes and commutativity degree of some finite non-abelian groups. In particular, we describe the commutativity degree of these groups both in the split and non-split case.
Keywords:
Class equation, commutativity degree, conjugacy class,
Competing interests
The authors have no competing interests.
Open Access Policy
This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Copyright
The authors have no competing interests.
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ISSN (Online): 2040-7467
ISSN (Print): 2040-7459 |
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