|
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
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
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
Linking options:
https://www.mathnet.ru/eng/pfmt728 https://www.mathnet.ru/eng/pfmt/y2020/i3/p55
|
|