TY - JOUR
ID - 8477
TI - On the commutativity degree in finite Moufang loops
JO - International Journal of Group Theory
JA - IJGT
LA - en
SN - 2251-7650
AU - Ahmadidelir, Karim
AD - Tabriz Branch, Islamic Azad University
Y1 - 2016
PY - 2016
VL - 5
IS - 3
SP - 37
EP - 47
KW - Loop theory
KW - Finite Moufang loops
KW - Commutativity degree in finite groups
DO - 10.22108/ijgt.2016.8477
N2 - 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.
UR - https://ijgt.ui.ac.ir/article_8477.html
L1 - https://ijgt.ui.ac.ir/article_8477_94d05d230f23cf1b5b857c0b3c5bdd37.pdf
ER -