α-NILPOTENT GROUPS DERIVED FROM HYPERGROUPS WITH ξ∗-RELATION

Abstract

This paper deals with hypergroups, as a generalization of classical groups.  An important tool in the theory of hyperstructures is the fundamental relation, which brings us into the classical algebra.  In this paper for an automorphism α we introduce and study the construction of α-nilpotent fundamental relation in hypergroups.  We will characterize α-nilpotent groups via strongly regular relations and several results on the topic are presented.