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

PFMT, 2020 Issue 3(44), Pages 55–60 (Mi pfmt728)

This article is cited in 1 paper

MATHEMATICS

On skew elements in polyadic groups of special form defined by cyclic substitution

A. M. Gal'mak

Mogilev State University of Food Technologies

Abstract: 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, substitution.

UDC: 512.548

Received: 14.05.2020



© Steklov Math. Inst. of RAS, 2024