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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| Date: | 2024 |
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| Language: | English |
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Lugansk National Taras Shevchenko University
2024
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| Journal Title: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-22992024-09-23T09:29:11Z On left-gyrotranslation groups of gyrogroups Suksumran, Teerapong Wattanapan, Jaturon permutation group, gyrogroup, left gyrotranslation, gyroautomorphism 20B99, 20N05 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. Lugansk National Taras Shevchenko University Chiang Mai University 2024-09-23 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2299 10.12958/adm2299 Algebra and Discrete Mathematics; Vol 38, No 1 (2024) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2299/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2299/1210 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2299/1209 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2299/1241 Copyright (c) 2024 Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics |
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| datestamp_date |
2024-09-23T09:29:11Z |
| collection |
OJS |
| language |
English |
| topic |
permutation group gyrogroup left gyrotranslation gyroautomorphism 20B99 20N05 |
| spellingShingle |
permutation group gyrogroup left gyrotranslation gyroautomorphism 20B99 20N05 Suksumran, Teerapong Wattanapan, Jaturon On left-gyrotranslation groups of gyrogroups |
| topic_facet |
permutation group gyrogroup left gyrotranslation gyroautomorphism 20B99 20N05 |
| format |
Article |
| author |
Suksumran, Teerapong Wattanapan, Jaturon |
| author_facet |
Suksumran, Teerapong Wattanapan, Jaturon |
| author_sort |
Suksumran, Teerapong |
| title |
On left-gyrotranslation groups of gyrogroups |
| title_short |
On left-gyrotranslation groups of gyrogroups |
| title_full |
On left-gyrotranslation groups of gyrogroups |
| title_fullStr |
On left-gyrotranslation groups of gyrogroups |
| title_full_unstemmed |
On left-gyrotranslation groups of gyrogroups |
| title_sort |
on left-gyrotranslation groups of gyrogroups |
| description |
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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2024 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2299 |
| work_keys_str_mv |
AT suksumranteerapong onleftgyrotranslationgroupsofgyrogroups AT wattanapanjaturon onleftgyrotranslationgroupsofgyrogroups |
| first_indexed |
2025-07-17T10:35:23Z |
| last_indexed |
2025-07-17T10:35:23Z |
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1837890036615348224 |