Document Type : Original Article
Department of Mathematics, Payame Noor University (PNU), Iran
Fundamental relations are one of the main tools in connection relation between hyperstructures theory and structures theory. In this paper, we introduce a general fundamental relation on any hypergroup in such a way that all fundamental relations are a special case of this relation. Also, this study considered the notation of the relation on the derivation of $k$-nilpotent groups from any hypergroups.