Journal of Prime Research in Mathematics

# Construction of middle nuclear square loops

Amir Khan
Department of Mathematics and Statistics, University of Swat, Swat, Pakistan.
$$^{1}$$Corresponding Author: amir.maths@gmail.com
Middle nuclear square loops are loops satisfying $$x(y(zz)) =(xy)(zz)$$ for all $$x, y$$ and $$z$$. We construct an infinite family of nonassociative noncommutative middle nuclear square loops whose smallest member is of order 12.