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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{BASM_2017_3_a0,
     author = {Halyna Krainichuk and Olena Tarkovska},
     title = {Semi-symmetric isotopic closure of some group varieties and the corresponding identities},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {3--22},
     publisher = {mathdoc},
     number = {3},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2017_3_a0/}
}
TY  - JOUR
AU  - Halyna Krainichuk
AU  - Olena Tarkovska
TI  - Semi-symmetric isotopic closure of some group varieties and the corresponding identities
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2017
SP  - 3
EP  - 22
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BASM_2017_3_a0/
LA  - en
ID  - BASM_2017_3_a0
ER  - 
%0 Journal Article
%A Halyna Krainichuk
%A Olena Tarkovska
%T Semi-symmetric isotopic closure of some group varieties and the corresponding identities
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2017
%P 3-22
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BASM_2017_3_a0/
%G en
%F BASM_2017_3_a0
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. http://geodesic.mathdoc.fr/item/BASM_2017_3_a0/