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

PFMT, 2020 Issue 2(43), Pages 64–68 (Mi pfmt713)

This article is cited in 2 papers

MATHEMATICS

On skew elements in polyadic groups of special form

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, 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.

UDC: 512.548

Received: 29.01.2020



© Steklov Math. Inst. of RAS, 2024