Construction of \(n\)-ary \((H,G)\)-hypergroups.
Let \((H,f)\) be an \(n\)-ary hypergroup and \((G,h)\) be an \(n\)-ary group derived from some binary group. Let \(K\) by the union of a family of non-empty disjoint subsets \(A_g\) of \(H\) uniquely indexed by elements of \(G\) in the way that \(A_e=H\). If the hyper-operation \(f\) is extended to \(K\) in the way that \(f(x_1^n)=A_{h(g_1^n)}\) for all \((x_1^n)\in A_{g_1}\times\cdots\times A_{g_n}\neq H^n\) the structure obtained is an \(n\)-ary hypergroup called an \(n\)-ary \((H,G)\)-hypergroup. Properties and the fundamental relation of such hypergroups are described.
scientific article; zbMATH DE number 6143504
scientific article