Group embedding of generalised Bol loops

Abstract

In this paper, special embedding of generalized Bol loops in groups is obtained. It is found that if the generalized Bol loop is specially embeddable in a group, each loop isotopic to it is also specially embeddable in the group. A generalized Bol loop obtained from a special subset of a group is specially embeddable in the homomorphic image of the group. The universal embedding of generalized Bol loops into free groups on n generators is obtained.