Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
K-loops. (Russian)
Authors: Basarab A. S.
Abstract
The loop $Q(\cdot)$ is a $K$-loop if in $Q(\cdot)$ the following identities are true $(x\cdot yJx)\cdot xz=x\cdot yz$ and $(y\cdot x)\cdot (J^{-1}xz\cdot x)=yz\cdot x$ ($Jx=x^{-1}$, $J^{-1}x={}^{-1}x$). We prove that in a $K$-loop $Q(\cdot)$ the kernel $N$ is non -- trivial, $N$ is a normal subloop in the loop $Q(\cdot)$, the quotient loop $Q/N(\cdot)$ is an abelian group and any $K$-loop with kernel of odd order is solvable. An examble of $K$-loop is constructed.Contents
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- Locally dissipative dynamical systems and some of their applications. (Russian)
- Conditions for the maximal multiplicity of an integral line of a differential system with homogeneities of $m$th order. (Russian)
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- K-loops. (Russian)
- Groups of automorphisms of medial quasigroups and medial fields. (Russian)
- On the spectrum of perturbed differential operators with periodic coefficients. (Russian)
- Parametric completeness in the logic of the simplest pseudo-Boolean algebra with incomparable elements. (Russian)
- Coefficient conditions for the coexistence of two singular points of summed multiplicity 4 in a finite part of a phase plane of a quadratic system. (Russian)
- On the kinds of two-dimensional multiregular partitions. (Russian)
- On a class of nonlocal generalized splines. (Russian)
- On the number of near neighbors in regular partitions of Lobachevskij space by compact polyhedra. (Russian)
- An approximation algorithm for matroids with coalitions. (English)
- On finite projection of nonstationary $M/GI/1$ queueing systems. (English)
- Numerical modeling of the process of high-velocity penetration of an obstacle. (Russian)
