Journal of Prime Research in Mathematics

Construction of middle nuclear square loops

Amir Khan
Department of Mathematics and Statistics, University of Swat, Swat, Pakistan.
Muhammad Shah
Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan.
Asif Ali
Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan.

\(^{1}\)Corresponding Author: amir.maths@gmail.com

Abstract

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.

Keywords:

Middle nuclear square loop, construction of loop, C-loops.