Geodesic
Semi-symmetric isotopic closure of some group varieties and the corresponding identities
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2017), pp. 3-22.

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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. 
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Halyna Krainichuk; Olena Tarkovska. Semi-symmetric isotopic closure of some group varieties and the corresponding identities. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2017), pp. 3-22. https://geodesic-test.mathdoc.fr/item/BASM_2017_3_a0/

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