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. 
@article{FPM_2023_24_4_a12,
     author = {N. A. Shchuchkin},
     title = {Finitely generated {Abelian} $n$-groups},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {217--237},
     publisher = {mathdoc},
     volume = {24},
     number = {4},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2023_24_4_a12/}
}
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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/