Fook Leong

All f-loops are groups

A Moufang loop L of order (r s, αi, ϵ Z + r≤3s≤3, αi≤4 and p i are distinct primes greater than 3) is called an f-loop if the equality of associators, (x y z) = (x zy z) is true for all x y zϵ L. It is proven in [9] that L is a group if r ≤ 2. In this paper, we generalise the result to r ≤ 3.