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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| Date: | 2022 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2022
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1772 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543139219636224 |
|---|---|
| author | Marín, V. Pinedo, H. |
| author_facet | Marín, V. Pinedo, H. |
| author_sort | Marín, V. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2022-10-14T16:01:17Z |
| 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. |
| first_indexed | 2025-12-02T15:35:10Z |
| format | Article |
| id | admjournalluguniveduua-article-1772 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:35:10Z |
| publishDate | 2022 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-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 |
| spellingShingle | groupoid direct product semidirect product solvable groupoid Primary 20L05; Secondary 20N02 18A32 Marín, V. Pinedo, H. Groupoids: Direct products, semidirect products and solvability |
| title | 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_short | Groupoids: Direct products, semidirect products and solvability |
| title_sort | groupoids: direct products, semidirect products and solvability |
| topic | groupoid direct product semidirect product solvable groupoid Primary 20L05; Secondary 20N02 18A32 |
| topic_facet | groupoid direct product semidirect product solvable groupoid Primary 20L05; Secondary 20N02 18A32 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1772 |
| work_keys_str_mv | AT marinv groupoidsdirectproductssemidirectproductsandsolvability AT pinedoh groupoidsdirectproductssemidirectproductsandsolvability |