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Problemy Fiziki, Matematiki i Tekhniki (Problems of Physics, Mathematics and Technics), 2020, Issue 2(43), Pages 64–68
(Mi pfmt713)
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This article is cited in 2 scientific papers (total 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.
Received: 29.01.2020
Citation:
A. M. Gal'mak, “On skew elements in polyadic groups of special form”, PFMT, 2020, no. 2(43), 64–68
Linking options:
https://www.mathnet.ru/eng/pfmt713 https://www.mathnet.ru/eng/pfmt/y2020/i2/p64
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