Geodesic
Finitely generated Abelian $n$-groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 24 (2023) no. 4, pp. 217-237
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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. 
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N. A. Shchuchkin. Finitely generated Abelian $n$-groups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 24 (2023) no. 4, pp. 217-237. http://geodesic.mathdoc.fr/item/FPM_2023_24_4_a12/

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