On left-gyrotranslation groups of gyrogroups
A gyrogroup is an algebraic structure whose operation is, in general, non-associative that shares some common properties with groups. In this paper, we prove that every gyrogroup induces a permutation group, called the left-gyrotranslation group, that can be used to understand the algebraic structur...
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| Дата: | 2024 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2024
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2299 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | A gyrogroup is an algebraic structure whose operation is, in general, non-associative that shares some common properties with groups. In this paper, we prove that every gyrogroup induces a permutation group, called the left-gyrotranslation group, that can be used to understand the algebraic structure of the gyrogroup itself. We also show several connections between gyrogroups and their left-gyrotranslation groups and give a few related examples, especially the left-gyrotranslation group of the famous Möbius gyrogroup in the complex plane. |
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