Classification of group isotopes according to their inverse properties
Coincidence of translation sets of the same directions in a quasigroup defines nine varieties: IP, CIP and mirror quasigroup varieties [9]. Their intersection with the variety of group isotopes is studied. In particular, it is proved that in the variety of group isotopes, the subvarieties of the mid...
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| Date: | 2020 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of NAS of Ukraine
2020
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| Online Access: | http://journals.iapmm.lviv.ua/ojs/index.php/APMM/article/view/apmm2020.18.48-61 |
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| Journal Title: | Prykladni Problemy Mekhaniky i Matematyky |
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Prykladni Problemy Mekhaniky i Matematyky| Summary: | Coincidence of translation sets of the same directions in a quasigroup defines nine varieties: IP, CIP and mirror quasigroup varieties [9]. Their intersection with the variety of group isotopes is studied. In particular, it is proved that in the variety of group isotopes, the subvarieties of the middle, left and right mirror quasigroups coincide with the subvarieties of commutative, left and right symmetric quasigroups respectively. Cite as: A. V. Lutsenko, “Classification of group isotopes according to their inverse properties,” Prykl. Probl. Mekh. Mat., Issue 18, 48–61 (2020), https://doi.org/10.15407/apmm2020.18.48-61 |
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