Title of article :
On the commutativity degree in finite Moufang loops
Author/Authors :
Ahmadidelir ، Karim - Islamic Azad University, Tabriz Branch
Abstract :
The commutativity degree, , of a finite group G G (i.e. the probability that two (randomly chosen) elements of G Gcommute 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 58 58 for a finite non-abelian group G G. In this paper, we will define the same concept for a finite non--abelian 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 Chein loops, and its modifications, this best upper bound is 2332 2332. So, our conjecture is that for any finite Moufang loop M M, Pr(M)≤2332 Pr(M)≤2332.
Keywords :
Loop theory , Finite Moufang loops , Commutativity degree in finite groups
Journal title :
International Journal of Group Theory
Journal title :
International Journal of Group Theory