Geodesic
Finitely generated Abelian $n$-groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 24 (2023) no. 4, pp. 217-237.

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - N. A. Shchuchkin
TI  - Finitely generated Abelian $n$-groups
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2023
SP  - 217
EP  - 237
VL  - 24
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2023_24_4_a12/
LA  - ru
ID  - FPM_2023_24_4_a12
ER  - 
%0 Journal Article
%A N. A. Shchuchkin
%T Finitely generated Abelian $n$-groups
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2023
%P 217-237
%V 24
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2023_24_4_a12/
%G ru
%F FPM_2023_24_4_a12
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/

[1] Artamonov V. A., Lektsii po algebre, III semestr, mekh-mat MGU, M., 2000

[2] Boschenko A. P., Schuchkin N. A., “Konechnye abelevy $n$-arnye gruppy”, Chebyshevskii sb., 12:2(38) (2011), 5–14 | MR

[3] Galmak A. M., “Poluabelevy $n$-arnye gruppy s idempotentami”, Vesnik VDU im. P. M. Masherava, 2 (12) (1999), 56–60

[4] Galmak A. M., $n$-arnye gruppy, v. I, Gomelskii gos. univ. im. F. Skoriny, Gomel, 2003

[5] Kurosh A. G., Teoriya grupp, Nauka, M., 1967 | MR

[6] Schuchkin N. A., “Polutsiklicheskie $n$-arnye gruppy”, Izv. GGU im. F. Skoriny, 3 (54) (2009), 186–194

[7] Schuchkin N. A., “Svobodnye abelevy $n$-arnye gruppy”, Chebyshevskii sb., 12:2(38) (2011), 163–170 | MR

[8] Schuchkin N. A., “Pryamoe proizvedenie $n$-arnykh grupp”, Chebyshevskii sb., 15:2 (2014), 101–121

[9] Schuchkin N. A., “Stroenie konechnykh abelevykh $n$-arnykh grupp”, Diskret. matem., 26:3 (2014), 144–159 | DOI

[10] Fuks L., Beskonechnye abelevy gruppy, v. 1, Mir, M., 1974

[11] Dörnte W., “Untersuchungen über einen verallgemeinerten Gruppenbegrieff”, Math. Z., 29 (1928), 1–19 | DOI | MR

[12] Dudek W. A., Michalski J., “On retrakts of polyadic groups”, Demonstratio Math., 17 (1984), 281–301 | MR | Zbl

[13] Post E. L., “Polyadic groups”, Trans. Amer. Math. Soc., 48 (1940), 208–350 | DOI | MR | Zbl

[14] Timm J., Kommutative $n$-Gruppen, Diss., Hamburg, 1967