Journal of Prime Research in Mathematics
Vol. 1 (2013), Issue 1, pp. 72 – 78
ISSN: 1817-3462 (Online) 1818-5495 (Print)
ISSN: 1817-3462 (Online) 1818-5495 (Print)
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
Copyright © 2013 Amir Khan, Muhammad Shah, Asif Ali. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Published: December, 2013.
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.