Канонічні та матричні задання квазігруп четвертого порядку
A quasigroup is called a loop if it has a neutral element. When it is denoted by 0, it is called a 0-loop. There are 4 0-loops of the fourth order, one of which is a Klein group, the other three are isomorphic to a cyclic group. The obtained results are: 1) every quasigroup of the fourth order has a...
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| Дата: | 2024 |
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| Автори: | , , |
| Формат: | Стаття |
| Опубліковано: |
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of NAS of Ukraine
2024
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| Теми: | |
| Онлайн доступ: | http://journals.iapmm.lviv.ua/ojs/index.php/APMM/article/view/apmm2024.22.95-105 |
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| Назва журналу: | Prykladni Problemy Mekhaniky i Matematyky |
Репозитарії
Prykladni Problemy Mekhaniky i Matematyky| Резюме: | A quasigroup is called a loop if it has a neutral element. When it is denoted by 0, it is called a 0-loop. There are 4 0-loops of the fourth order, one of which is a Klein group, the other three are isomorphic to a cyclic group. The obtained results are: 1) every quasigroup of the fourth order has a unique canonical decomposition over exactly one of these four 0-loops; 2) every quasigroup of the fourth order has a unique matrix canonical decomposition over either a cyclic group or a Klein group; 3) the corresponding formulas and examples for their use are given. Cite as: F. M. Sokhatsky, H. V. Krainichuk, V. A. Luzhetsky, “Canonical and matrix figuration of quasigroups of the fourth order,” Prykl. Probl. Mekh. Mat., Issue 22, 95–105 (2024) (in Ukrainian), https://doi.org/10.15407/apmm2024.22.95-105 |
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