Geodesic
On skew elements in polyadic groups of special form
Problemy fiziki, matematiki i tehniki, no. 2 (2020), pp. 64-68.

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

The article goes on with a study of skew elements in polyadic groups of special form, 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 of $A^k$ $n$-ary group $\langle A,\eta\rangle$ by substitution $\sigma\in\mathbf{S}_k$ which order divides $l-1$ and $n$-ary operation $\eta$. In particular a theorem has been proved that allows us to determine a skew element for each element of $l$-ary group of a special form, the skew element being formulated by means of a inverse sequences of $n$-ary group on Cartesian power of which the given $l$-ary group is constructed.
Keywords: polyadic operation, $n$-ary group, skew element, inverse sequence. 
@article{PFMT_2020_2_a10,
     author = {A. M. Gal'mak},
     title = {On skew elements in polyadic groups of special form},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {64--68},
     publisher = {mathdoc},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2020_2_a10/}
}
TY  - JOUR
AU  - A. M. Gal'mak
TI  - On skew elements in polyadic groups of special form
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2020
SP  - 64
EP  - 68
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2020_2_a10/
LA  - ru
ID  - PFMT_2020_2_a10
ER  - 
%0 Journal Article
%A A. M. Gal'mak
%T On skew elements in polyadic groups of special form
%J Problemy fiziki, matematiki i tehniki
%D 2020
%P 64-68
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2020_2_a10/
%G ru
%F PFMT_2020_2_a10
A. M. Gal'mak. On skew elements in polyadic groups of special form. Problemy fiziki, matematiki i tehniki, no. 2 (2020), pp. 64-68. http://geodesic.mathdoc.fr/item/PFMT_2020_2_a10/

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

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

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

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

[5] S.A. Rusakov, Algebraicheskie n-arnye sistemy, Navuka i tekhnika, Mn., 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] W. Dörnte, “Untersuchungen über einen verallgemeinerten Gruppenbegrieff”, Math. Z., 29 (1928), 1–19 | MR | Zbl

[9] A.M. Galmak, Yu.I. Kulazhenko, M.V. Selkin, “Kosye elementy v poliadicheskikh gruppakh spetsialnogo vida”, Izvestiya Gomelskogo gosudarstvennogo universiteta imeni F. Skoriny, 2019, no. 6 (117), 186–188 | Zbl

[10] A.M. Galmak, Kongruentsii poliadicheskikh grupp, Belaruskaya navuka, Minsk, 1999, 182 pp.