Groupoids: Direct products, semidirect products and solvability
We present some constructions of groupoids such as: direct product, semidirect product and give necessary and sufficient conditions for a groupoid to be embedded into a direct product of groupoids. Also, we establish necessary and sufficient conditions to determine when a semidirect product is direc...
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| Дата: | 2022 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2022
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1772 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-17722022-10-14T16:01:17Z Groupoids: Direct products, semidirect products and solvability Marín, V. Pinedo, H. groupoid, direct product, semidirect product, solvable groupoid Primary 20L05; Secondary 20N02, 18A32 We present some constructions of groupoids such as: direct product, semidirect product and give necessary and sufficient conditions for a groupoid to be embedded into a direct product of groupoids. Also, we establish necessary and sufficient conditions to determine when a semidirect product is direct. Finally the notion of solvable groupoid is introduced and studied, in particular it is shown that a finite groupoid \(\mathcal{G}\) is solvable if and only if its isotropy groups are. Lugansk National Taras Shevchenko University 2022-10-14 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1772 10.12958/adm1772 Algebra and Discrete Mathematics; Vol 33, No 2 (2022) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1772/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1772/837 Copyright (c) 2022 Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics |
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| datestamp_date |
2022-10-14T16:01:17Z |
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OJS |
| language |
English |
| topic |
groupoid direct product semidirect product solvable groupoid Primary 20L05; Secondary 20N02 18A32 |
| spellingShingle |
groupoid direct product semidirect product solvable groupoid Primary 20L05; Secondary 20N02 18A32 Marín, V. Pinedo, H. Groupoids: Direct products, semidirect products and solvability |
| topic_facet |
groupoid direct product semidirect product solvable groupoid Primary 20L05; Secondary 20N02 18A32 |
| format |
Article |
| author |
Marín, V. Pinedo, H. |
| author_facet |
Marín, V. Pinedo, H. |
| author_sort |
Marín, V. |
| title |
Groupoids: Direct products, semidirect products and solvability |
| title_short |
Groupoids: Direct products, semidirect products and solvability |
| title_full |
Groupoids: Direct products, semidirect products and solvability |
| title_fullStr |
Groupoids: Direct products, semidirect products and solvability |
| title_full_unstemmed |
Groupoids: Direct products, semidirect products and solvability |
| title_sort |
groupoids: direct products, semidirect products and solvability |
| description |
We present some constructions of groupoids such as: direct product, semidirect product and give necessary and sufficient conditions for a groupoid to be embedded into a direct product of groupoids. Also, we establish necessary and sufficient conditions to determine when a semidirect product is direct. Finally the notion of solvable groupoid is introduced and studied, in particular it is shown that a finite groupoid \(\mathcal{G}\) is solvable if and only if its isotropy groups are. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2022 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1772 |
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AT marinv groupoidsdirectproductssemidirectproductsandsolvability AT pinedoh groupoidsdirectproductssemidirectproductsandsolvability |
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2025-07-17T10:37:12Z |
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2025-07-17T10:37:12Z |
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1837890150008356865 |