Certain numerical results in non‑associative structures

The finite non-commutative and non-associative algebraic structures are indeed one of the special structures for their proba-bilistic results in some branches of mathematics. For a given integer n ≥ 2 , the nth-commutativity degree of a finite algebraic structure S, denoted by Pn(S) , is the probability that for chosen randomly two elements x and y of S, the relator xny = yxn holds. This degree is specially a recognition tool in identifying such structures and studied for associative algebraic struc-tures during the years. In this paper, we study the nth-commutativity degree of two infinite classes of finite loops, which are non-commutative and non-associative. Also by deriving explicit expressions for nth-commutativity degree of these loops, we will obtain best upper bounds for this probability.