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: | , , |
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| Format: | Article |
| Language: | English |
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Amirkabir University of Technology
2024-01-01
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| Series: | AUT Journal of Mathematics and Computing |
| Subjects: | |
| Online Access: | https://ajmc.aut.ac.ir/article_5063_983eca1af8bdaee5215d91067efdf2f8.pdf |
| Summary: | 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. |
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| ISSN: | 2783-2449 2783-2287 |