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On recursively differentiable $k$-quasigroups
Parascovia Syrbu, Elena Cuzneţov Moldova State University, Department of Mathematics
Abstract:
Recursive differentiability of linear $k$-quasigroups $(k\geq 2)$ is studied in the present work. A $k$-quasigroup is recursively $r$-differentiable ($r$ is a natural number) if its recursive derivatives of order up to $r$ are quasigroup operations. We give necessary and sufficient conditions of recursive $1$-differentiability (respectively, $r$-differentiability) of the $k$-group $(Q,B)$, where $B(x_1,..., x_k)=x_1 \cdot x_2 \cdot ... \cdot x_k , \forall x_1 , x_2 ,..., x_k \in Q,$ and $(Q, \cdot)$ is a finite binary group (respectively, a finite abelian binary group). The second result is a generalization of a known criterion of recursive $r$-differentiability of finite binary abelian groups [4]. Also we consider a method of construction of recursively $r$-differentiable finite binary quasigroups of high order $r$. The maximum known values of the parameter $r$ for binary quasigroups of order up to $200$ are presented.
Keywords and phrases:
$k$-ary quasigroup, recursive derivative, recursively differentiable quasigroup.
Received: 21.07.2022
Citation:
Parascovia Syrbu, Elena Cuzneţov, “On recursively differentiable $k$-quasigroups”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2022, no. 2, 68–75
Linking options:
https://www.mathnet.ru/eng/basm573 https://www.mathnet.ru/eng/basm/y2022/i2/p68
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Abstract page: | 337 | Full-text PDF : | 35 | References: | 15 |
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