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JOURNALS // Problemy Fiziki, Matematiki i Tekhniki (Problems of Physics, Mathematics and Technics) // Archive

PFMT, 2022 Issue 1(50), Pages 55–61 (Mi pfmt827)

MATHEMATICS

On sets of generators of $l$-ary group $\langle A^k, [\ ]_{l,\sigma,k}\rangle$. IV

A. M. Gal'mak

Belarusian State University of Food and Chemical Technologies, Mogilev

Abstract: The article goes on with the studies on the described earlier 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 $l\geqslant2$ and arbitrary substitution $\sigma$ from the set $\mathbf{S}_k$ of all substitutions of the set $\{1, 2, \dots, k\}$.

Keywords: group, $l$-ary group, set of generators.

UDC: 512.548

Received: 08.02.2022

DOI: 10.54341/20778708_2022_1_50_55



© Steklov Math. Inst. of RAS, 2024