Construction of $n$-ary $(H,G)$-hypergroups

Abstract

In this paper, we shall define the concepts of completion and complete part with respect to $n$-ary $(H,G)$-hypergroups. Moreover, we present a way to obtain a new $n$-ary hypergroup, starting with other $n$-ary hypergroups. Finally, we introduce the fundamental relation of an $n$-ary hypergroup and prove some results. Examples in known classes of $n$-ary $(H,G)$-hypergroups are also investigated.