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Semi-symmetric isotopic closure of some group varieties and the corresponding identities
Authors: Halyna Krainichuk, Olena Tarkovska
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Abstract
Four families of pairwise equivalent identities are given and analyzed. Every identity from each of these families defines one of the following varieties: 1)~the semi-symmetric isotopic closure of the variety of all Boolean groups; 2)~the semi-symmetric isotopic closure of the variety of all Abelian groups; 3)~the semi-symmetric isotopic closure of the variety of all groups; 4)~the variety of all semi-symmetric quasigroups. It is proved that these varieties are different and form a chain. Quasigroups belonging to these varieties are described. In particular, quasigroups from 1) and 2) varieties are medial and in addition, they are either groups or non-commutative semi-symmetric quasigroups.V. Stus Donetsk National University
Department of mathematical analysis
and differential equations
21000 Vinnytsia, Ukraine
E-mail: ,
Department of mathematical analysis
and differential equations
21000 Vinnytsia, Ukraine
E-mail: ,
Fulltext
– 0.19 Mb
Contents
- Semi-symmetric isotopic closure of some group varieties and the corresponding identities
- Factorizations in the rings of the block matrices
- Inclusion Properties of Certain Subclass of Univalent Meromorphic Functions Defined by a Linear Operator Associated with the $\lambda$-Generalized Hurwitz-Lerch Zeta Function
- Interpolating Bézier spline surfaces with local control
- A Note on the Equivalence of Control Systems on Lie Groups
- Viscous flow through a porous medium filled by liquid with varying viscosity
- Invariant conditions of stability of unperturbed motion governed by some differential systems in the plane
- A Note on 2-Hypersurfaces of the Nearly Kählerian Six-Sphere
- Post-quantum No-key Protocol
- Some estimates for angular derivative at the boundary
