On the core of some classes of generalised Bol-Moufang loops

Abstract

This study centers on properties of the core of some classes of generalized Bol-Moufang loops wherein a construction of a generalized Bol loop is presented. Several properties of the core of generalized Bol loops are established. Some of these properties inform that the core of generalized Bol loops belongs to the variety of Left Symmetric Left Distributive (LSLD) groupoid and therefore, a rack. A necessary and sufficient condition for the core of half-Bol loops to be medial is given with proof. The core of the inverse property (IP) generalized Moufang loop with universal α-elasticity is examined.