Finitely Generated Abelian n-Ary Groups

In this paper, the isomorphism of a finitely generated Abelian n-ary group and of a direct product of a finite number of indecomposable Abelian semi-cyclic n-ary groups, being partly finite primary and partly infinite ones, is proved. A complete system of invariants for finitely generated Abelian n-ary groups is found. We point out a necessary and sufficient condition for a direct product of infinite Abelian semi-cyclic n-ary groups to be a free n-ary group in the class of Abelian n-ary groups. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.