On a class of automorphic loops

Abstract

We introduce a new class of automorphic loops (L; *) which is constructed on a given group (G; .) by adjoining an induced binary operation * : G × G →L defined by the rule, *(x; y) = x * y = x . ɸ(y) for ɸ ϵ Aut(G), for all x, y ϵ G. In this paper, we extend the study of the class of automorphic loops. We also characterize the loop (L; *) by Aut(L).