MATHEMATICS

Polyadic quotient groups of polyadic groups of special form. I

A. M. Gal'mak

Belarusian State University of Food and Chemical Technologies, Mogilev

Abstract: The article studies of $l$-ary quotient groups of polyadic groups of special form, that is 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 substitution $\sigma\in\mathbf{S}_k$ which order divides $l-1$ and $n$-ary operation $\eta$.

Keywords: polyadic operation, semiinvariant $l$-ary subgroup, $n$-semiinvariant $l$-ary subgroup, quotient group, congruence, coset.

UDC: 512.548

Received: 04.08.2025

DOI: 10.54341/20778708_2025_3_64_84