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Bul. Acad. Ştiinţe Repub. Mold. Mat., 2017, Number 3, Pages 3–22 (Mi basm461)  

Semi-symmetric isotopic closure of some group varieties and the corresponding identities

Halyna Krainichuk, Olena Tarkovska

V. Stus Donetsk National University, Department of mathematical analysis and differential equations, 21000 Vinnytsia, Ukraine

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.

Keywords and phrases: group, quasigroup, identity, isotopic closure, variety, totally symmetric, semi-symmetric, commutative.

Funding Agency Grant Number
State Fund For Fundamental Research F71/47-2017
Publications are based on the research provided by the grant support of the State Fund For Fundamental Research, project no. F71/472017.


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Document Type: Article
MSC: 34C05, 58F14
Received: 30.11.2016
Language: English

Citation: Halyna Krainichuk, Olena Tarkovska, “Semi-symmetric isotopic closure of some group varieties and the corresponding identities”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2017, no. 3, 3–22

Citation in format AMSBIB
\Bibitem{KraTar17}
\by Halyna~Krainichuk, Olena~Tarkovska
\paper Semi-symmetric isotopic closure of some group varieties and the corresponding identities
\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.
\yr 2017
\issue 3
\pages 3--22
\mathnet{http://mi.mathnet.ru/basm461}


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