Geodesic
Powers in $l$-ary groups of a special form.~I
Problemy fiziki, matematiki i tehniki, no. 2 (2023), pp. 47-51.

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The article deals with powers in polyadic groups of a special form, that is in polyadic groups with $l$-ary operation $\eta_{s,\sigma,k}$, that is called polyadic operation of a special form and is defined on Cartesian power of $A^k$ $n$-ary group $\langle A,\eta\rangle$ by substitution $\sigma\in\mathbf{S}_k$ and $n$-ary operation $\eta$.
Keywords: polyadic operation, $n$-ary group, power. 
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A. M. Gal'mak. Powers in $l$-ary groups of a special form.~I. Problemy fiziki, matematiki i tehniki, no. 2 (2023), pp. 47-51. http://geodesic.mathdoc.fr/item/PFMT_2023_2_a8/

[1] A.M. Galmak, A.D. Rusakov, “O poliadicheskikh operatsiyakh na dekartovykh stepenyakh”, Izvestiya Gomelskogo gosudarstvennogo universiteta imeni F. Skoriny, 2014, no. 3 (84), 35–40

[2] A.M. Galmak, Mnogomestnye operatsii na dekartovykh stepenyakh, Izd. tsentr BGU, Minsk, 2009, 265 pp.

[3] E.L. Post, “Polyadic groups”, Trans. Amer. Math. Soc., 48:2 (1940), 208–350 | DOI | MR | Zbl

[4] A.M. Galmak, “O razreshimosti uravnenii v $\langle A^k, \eta_{s,\sigma,k}\rangle$”, Vesnik MDU im. A.A. Kulyashova, 2018, no. 1 (51), 4–10 | MR

[5] S.A. Rusakov, Algebraicheskie n-arnye sistemy, Navuka i tekhnika, Minsk, 1992, 245 pp.

[6] A.M. Galmak, $n$-Arnye gruppy, v. 1, GGU im. F. Skoriny, Gomel, 2003, 202 pp.

[7] A.M. Galmak, $n$-Arnye gruppy, v. 2, Izd. tsentr BGU, Minsk, 2007, 324 pp.

[8] N.A. Schuchkin, Vvedenie v teoriyu $n$-grupp, Print, Volgograd, 2019, 236 pp.

[9] W. Dornte, “Untersuchungen uber einen verallgemeinerten Gruppenbegrieff”, Math. Z., 29 (1928), 1–19 | DOI | MR

[10] A.M. Galmak, Yu.I. Kulazhenko, M.V. Selkin, “Kosye elementy v poliadicheskikh gruppakh spetsialnogo vida”, Vesnik MDU im. A.A. Kulyashova, 2020, no. 2 (56), 13–20