2024 : 2 : 21
Sakineh Rahbariyan

Sakineh Rahbariyan

Academic rank: Assistant Professor
ORCID: https://orcid.org/0000-0001-7193-3850
Education: PhD.
ScopusId: 52364509200
Faculty: Science
Address: Arak University
Phone:

Research

Title
On the commutativity degree of ${\rm PSL}(2, q)$
Type
Presentation
Keywords
Commutativity degree, Non-abelian group, Simple group
Year
2022
Researchers Sakineh Rahbariyan

Abstract

Let $G$ be a finite group. The commutativity degree of $G$ denoted by $P(G)$ is the probability of two group elements that commute. As a matter of fact, if $C=\{(x, y)\in G\times G \ | \ xy=yx\}$, then $P(G)=\frac{|C|}{|G|^2}$. In this paper, we are going to find the commutativity degree of the projective special linear group ${\rm PSL}(2, q)$, where $q$ is a power of a prime $p$, and $q\equiv 0$ $\pmod 4$.