Classification of gyrogroups of orders at most 31
A gyrogroup is defined as having a binary operation containing an identity element such that each element has an inverse. Furthermore, for each pair (a,b) of elements of this structure, there exists an automorphism gyr[a,b] with the property that left associativity and the left loop property are sa...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Amirkabir University of Technology
2024-01-01
|
| Series: | AUT Journal of Mathematics and Computing |
| Subjects: | |
| Online Access: | https://ajmc.aut.ac.ir/article_5063_983eca1af8bdaee5215d91067efdf2f8.pdf |
| _version_ | 1797307105464549376 |
|---|---|
| author | Ali Ashrafi Kurosh Mavaddat Nezhaad Mohammad Salahshour |
| author_facet | Ali Ashrafi Kurosh Mavaddat Nezhaad Mohammad Salahshour |
| author_sort | Ali Ashrafi |
| collection | DOAJ |
| description | A gyrogroup is defined as having a binary operation containing an identity element such that each element has an inverse. Furthermore, for each pair (a,b) of elements of this structure, there exists an automorphism gyr[a,b] with the property that left associativity and the left loop property are satisfied. Since each gyrogroup is a left Bol loop, some results of Burn imply that all gyrogroups of orders p,2p, and p2, where p is a prime number, are groups. This paper aims to classify gyrogroups of orders 8, 12, 15, 18, 20, 21, and 28. |
| first_indexed | 2024-03-08T00:52:30Z |
| format | Article |
| id | doaj.art-fff26c4b68d34f1c865cffc974380e1a |
| institution | Directory Open Access Journal |
| issn | 2783-2449 2783-2287 |
| language | English |
| last_indexed | 2024-03-08T00:52:30Z |
| publishDate | 2024-01-01 |
| publisher | Amirkabir University of Technology |
| record_format | Article |
| series | AUT Journal of Mathematics and Computing |
| spelling | doaj.art-fff26c4b68d34f1c865cffc974380e1a2024-02-14T19:42:47ZengAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24492783-22872024-01-0151111810.22060/ajmc.2023.21939.11255063Classification of gyrogroups of orders at most 31Ali Ashrafi0Kurosh Mavaddat Nezhaad1Mohammad Salahshour2Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, IranDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, IranDepartment of Mathematics, Savadkooh Branch, Islamic Azad University, Savadkooh, IranA gyrogroup is defined as having a binary operation containing an identity element such that each element has an inverse. Furthermore, for each pair (a,b) of elements of this structure, there exists an automorphism gyr[a,b] with the property that left associativity and the left loop property are satisfied. Since each gyrogroup is a left Bol loop, some results of Burn imply that all gyrogroups of orders p,2p, and p2, where p is a prime number, are groups. This paper aims to classify gyrogroups of orders 8, 12, 15, 18, 20, 21, and 28.https://ajmc.aut.ac.ir/article_5063_983eca1af8bdaee5215d91067efdf2f8.pdfgyrogroupleft bol loopgyroautomorphism |
| spellingShingle | Ali Ashrafi Kurosh Mavaddat Nezhaad Mohammad Salahshour Classification of gyrogroups of orders at most 31 AUT Journal of Mathematics and Computing gyrogroup left bol loop gyroautomorphism |
| title | Classification of gyrogroups of orders at most 31 |
| title_full | Classification of gyrogroups of orders at most 31 |
| title_fullStr | Classification of gyrogroups of orders at most 31 |
| title_full_unstemmed | Classification of gyrogroups of orders at most 31 |
| title_short | Classification of gyrogroups of orders at most 31 |
| title_sort | classification of gyrogroups of orders at most 31 |
| topic | gyrogroup left bol loop gyroautomorphism |
| url | https://ajmc.aut.ac.ir/article_5063_983eca1af8bdaee5215d91067efdf2f8.pdf |
| work_keys_str_mv | AT aliashrafi classificationofgyrogroupsofordersatmost31 AT kuroshmavaddatnezhaad classificationofgyrogroupsofordersatmost31 AT mohammadsalahshour classificationofgyrogroupsofordersatmost31 |