Relations on Groups, Polygroups and Hypergroups

Abstract

In a classical algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two elements is a set. By using a certain type of equivalence relations, we can connect semihypergroups to semigroups and hypergroups (polygroups) to groups. These equivalence relations are called strongly regular relations. In this paper, we review some strongly regular relations on hyperstructures and we give some their applications.