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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2017, Number 3, Pages 3–22
(Mi basm461)
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This article is cited in 1 scientific paper (total in 1 paper)
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.
Received: 30.11.2016
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
Linking options:
https://www.mathnet.ru/eng/basm461 https://www.mathnet.ru/eng/basm/y2017/i3/p3
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Abstract page: | 148 | Full-text PDF : | 80 | References: | 30 |
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