Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
On recursively differentiable k-quasigroups
Authors: Sîrbu Parascovia, Cuzneţov Elena
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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 \cite{IzbashSyrbu}. 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.Moldova State University,
Department of Mathematics
E-mail: ,
Department of Mathematics
E-mail: ,
DOI
https://doi.org/10.56415/basm.y2022.i2.p68Fulltext
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Contents
- Isostrophy Bryant-Schneider Group-Invariant of Bol Loops
- On the solubility of a class of two-dimensional integral equations on a quarter plane with monotone nonlinearity
- Nuclear Identification of Some New Loop Identities of Length Five
- B-spline approximation of discontinuous functions defined on a closed contour in the complex plane
- On recursively differentiable k-quasigroups
- Limits of solutions to the semilinear plate equation with small parameter
- Asymptotic Behavior of Homogeneous Linear Recurrent Processes and Their Perturbations
