AUTOTOPIC CHARACTERISATION OF RIGHT CHEBAN LOOP

CHARACTERISATION OF RIGHT CHEBAN LOOP

Abstract

Some fundamental properties of right Cheban loop are established in the present study in relation to the autotopism of right Cheban loop. It is found that the autotopism is a right pseudo-automorphism with companion $c=u\dot vu^{-1}$. The autotopism and pseudo-automorphism are characterized in terms of the right and left translation. Thus, necessary and sufficient conditions are established for the Moufang part of right Cheban loops to be an autotopism and pseudo-automorphism with companion $c=(x^3)^{-1}\cdot x^{-1} x^3$. The study also describes the behaviour of the pseudo-automorphism of the right Cheban loops on the nuclei and Moufang part of the right Cheban loops.