On embedding groups into digroups
An idea of the notion of a digroup which generalizes groups and has close relationships with the dimonoids, trioids, Leibniz algebras and other structures was proposed by J.-L. Loday. In terms of digroups, Kinyon obtained an analogue of Lie’s third theorem for the class of so-called split Leibniz al...
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| Дата: | 2025 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2025
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2364 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | An idea of the notion of a digroup which generalizes groups and has close relationships with the dimonoids, trioids, Leibniz algebras and other structures was proposed by J.-L. Loday. In terms of digroups, Kinyon obtained an analogue of Lie’s third theorem for the class of so-called split Leibniz algebras. In this paper, we use group operations (semigroup operations) to construct new digroups (dimonoids) and show that any group (semigroup) can be embedded into a suitable non-trivial digroup (dimonoid). We present a universal extension for an arbitrary dimonoid, give a construction of the free abelian generalized digroup and characterize the least group congruence on it. We also describe the least abelian digroup congruence on the free generalized digroup. |
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