Characterizations of Automorphic Loops

Abstract

The notion of a new class of automorphic loops was introduced in [1] as a quasigroup with right identity element e. In this paper, we extend the study of the class of automorphic loops. We decompose the class of automorphic loops into automorphic
abelian and non-abelian subclasses. We search within a subclass of abelian automorphic loops, the families of left Bol/ right Bol and Moufang loops with their characterizations.