On the commutativity degree in finite Moufang loops

The textit{commutativity degree}, Pr(G) Pr(G) , of a finite group G G (i.e. the probability that two (randomly chosen) elements of G 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) Pr(G) is frac58 frac58 for a finite non--abelian group G G .
In this paper, we will define the same concept for a finite non--abelian textit{Moufang loop} M M and try to give a best upper bound for Pr(M) 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 frac2332 frac2332 . So, our conjecture is that for any finite Moufang loop M M , Pr(M)leqfrac2332 Pr(M)leqfrac2332 .
Also, we will obtain some results related to the Pr(M) 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.