Construction of Ternary H v -groups and Ternary P-hyperoperations

Abstract

In this paper, we study the concept of ternary H v -groups and some their properties. We give some examples of ternary H v -groups. Also, we consider the fundamental relation β* on a ternary H v -group and prove that β* is a compatible relation on a ternary H v -group. In addition, we define the P-hyperoperation, and then, we construct a new ternary H v -group.