@article {
author = {Ahmadidelir, Karim},
title = {On the commutativity degree in finite Moufang loops},
journal = {International Journal of Group Theory},
volume = {5},
number = {3},
pages = {37-47},
year = {2016},
publisher = {University of Isfahan},
issn = {2251-7650},
eissn = {2251-7669},
doi = {10.22108/ijgt.2016.8477},
abstract = {The \textit{commutativity degree}, $Pr(G)$, of a finite group $G$ (i.e. the probability that two (randomly chosen) elements of $G$ commute with respect to its operation)) has been studied well by many authors. It is well-known that the best upper bound for $Pr(G)$ is $\frac{5}{8}$ for a finite non--abelian group $G$. In this paper, we will define the same concept for a finite non--abelian \textit{Moufang loop} $M$ and try to give a best upper bound for $Pr(M)$. We will prove that for a well-known class of finite Moufang loops, named \textit{Chein loops}, and its modifications, this best upper bound is $\frac{23}{32}$. So, our conjecture is that for any finite Moufang loop $M$, $Pr(M)\leq \frac{23}{32}$. Also, we will obtain some results related to the $Pr(M)$ and ask the similar questions raised and answered in group theory about the relations between the structure of a finite group and its commutativity degree in finite Moufang loops.},
keywords = {Loop theory,Finite Moufang loops,Commutativity degree in finite groups},
url = {https://ijgt.ui.ac.ir/article_8477.html},
eprint = {https://ijgt.ui.ac.ir/article_8477_94d05d230f23cf1b5b857c0b3c5bdd37.pdf}
}