Geodesic
On skew elements in polyadic groups of special form defined by cyclic substitution
Problemy fiziki, matematiki i tehniki, no. 3 (2020), pp. 55-60.

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The article goes on with a study of skew elements in polyadic groups of special form defined by cyclic substitution, that is, in polyadic groups with $l$-ary operation $\eta_{s,\sigma,k}$ that is called polyadic operation of special form and is defined on Cartesian power $A^k$ of $n$-ary group $\langle A,\eta\rangle$ by cyclic substitution $\sigma\in\mathbf{S}_k$ satisfying the condition $\sigma^l=\sigma$, and $n$-ary operation $\eta$. As corollaries the results for polyadic groups were obtained. These polyadic groups are of special form with $l$-ary operation $\eta_{s,\sigma,k}$ in which $\sigma$ is a cycle such that its length devides $l-1$, in particular, $\sigma$ may be cycle of the form $(12\dots k)$.
Keywords: polyadic operation, $n$-ary group, skew element
Mots-clés : substitution. 
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A. M. Gal'mak. On skew elements in polyadic groups of special form defined by cyclic substitution. Problemy fiziki, matematiki i tehniki, no. 3 (2020), pp. 55-60. http://geodesic.mathdoc.fr/item/PFMT_2020_3_a8/

[1] A.M. Galmak, “O kosykh elementakh v poliadicheskikh gruppakh spetsialnogo vida”, Problemy fiziki, matematiki i tekhniki, 2020, no. 2(43), 64–68

[2] A.M. Galmak, A.D. Rusakov, “O poliadicheskikh operatsiyakh na dekartovykh stepenyakh”, Izvestiya GGU im. F. Skoriny, 2014, no. 3(84), 35–39

[3] 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

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

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

[6] S.A. Rusakov, Algebraicheskie $n$-arnye sistemy, Navuka i tekhnika, Mn., 1992, 245 pp.

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

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

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