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Problemy Fiziki, Matematiki i Tekhniki (Problems of Physics, Mathematics and Technics), 2020, Issue 3(44), Pages 55–60 (Mi pfmt728)  

This article is cited in 1 scientific paper (total 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
Full-text PDF (342 kB) Citations (1)
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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.
Received: 14.05.2020
Document Type: Article
UDC: 512.548
Language: Russian
Citation: A. M. Gal'mak, “On skew elements in polyadic groups of special form defined by cyclic substitution”, PFMT, 2020, no. 3(44), 55–60
Citation in format AMSBIB
\Bibitem{Gal20}
\by A.~M.~Gal'mak
\paper On skew elements in polyadic groups of special form defined by cyclic substitution
\jour PFMT
\yr 2020
\issue 3(44)
\pages 55--60
\mathnet{http://mi.mathnet.ru/pfmt728}
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  • This publication is cited in the following 1 articles:
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