Geodesic
On sets of generators of $l$-ary group $\langle A^k, [\ ]_{l,\sigma,k}\rangle$.~III
Problemy fiziki, matematiki i tehniki, no. 4 (2021), pp. 76-80.

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

The article goes on with the studies on the earlier described relationship between sets of generators in group $A$ and sets of generators in polyadic group $\langle A^k, [\ ]_{l,\sigma,k}\rangle$ with $l$-ary operation $[\ ]_{l,\sigma,k}$, that is defined on Cartesian power $A^k$ of group $A$ for arbitrary integer $l\geqslant 2$ and arbitrary substitution $\sigma$ from the set $\mathbf{S}_k$ of all substitutions of the set $\{1, 2, \dots, k\}$.
Mots-clés : group
Keywords: $l$-ary group, set of generators. 
@article{PFMT_2021_4_a11,
     author = {A. M. Gal'mak},
     title = {On sets of generators of $l$-ary group $\langle A^k, [\ ]_{l,\sigma,k}\rangle${.~III}},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {76--80},
     publisher = {mathdoc},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2021_4_a11/}
}
TY  - JOUR
AU  - A. M. Gal'mak
TI  - On sets of generators of $l$-ary group $\langle A^k, [\ ]_{l,\sigma,k}\rangle$.~III
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2021
SP  - 76
EP  - 80
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2021_4_a11/
LA  - ru
ID  - PFMT_2021_4_a11
ER  - 
%0 Journal Article
%A A. M. Gal'mak
%T On sets of generators of $l$-ary group $\langle A^k, [\ ]_{l,\sigma,k}\rangle$.~III
%J Problemy fiziki, matematiki i tehniki
%D 2021
%P 76-80
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2021_4_a11/
%G ru
%F PFMT_2021_4_a11
A. M. Gal'mak. On sets of generators of $l$-ary group $\langle A^k, [\ ]_{l,\sigma,k}\rangle$.~III. Problemy fiziki, matematiki i tehniki, no. 4 (2021), pp. 76-80. http://geodesic.mathdoc.fr/item/PFMT_2021_4_a11/

[1] A.M. Galmak, “O porozhdayuschikh mnozhestvakh $l$-arnoi gruppy. $\langle A^k,[\,]_{l,\sigma,k}\rangle$. I”, Problemy fiziki, matematiki i tekhniki, 2021, no. 2 (47), 69–78

[2] A.M. Galmak, “O porozhdayuschikh mnozhestvakh $l$-arnoi gruppy. $\langle A^k,[\,]_{l,\sigma,k}\rangle$. II”, Problemy fiziki, matematiki i tekhniki, 2021, no. 3 (48), 63–72

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

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

[5] A.A. Bukhshtab, Teoriya chisel, Prosveschenie, M., 1966, 384 pp.

[6] G.S.M. Kokseter, U.O.Dzh. Mozer, Porozhdayuschie elementy i opredelyayuschie sootnosheniya diskretnykh grupp, Nauka, M., 1980, 240 pp.

[7] D. Gorenstein, Konechnye prostye gruppy. Vvedenie v ikh klassifikatsiyu, Mir, M., 1985, 352 pp.