@article {
author = {Ashrafi, Ali and Mavaddat Nezhaad, Kurosh and Salahshour, Mohammad},
title = {Classification of gyrogroups of orders at most 31},
journal = {AUT Journal of Mathematics and Computing},
volume = {5},
number = {1},
pages = {11-18},
year = {2024},
publisher = {Amirkabir University of Technology},
issn = {2783-2449},
eissn = {2783-2287},
doi = {10.22060/ajmc.2023.21939.1125},
abstract = {A gyrogroup is defined as having a binary operation $\star$ 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 ${\mathrm{gyr}}[a,b]$ 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 $p^2$, where $p$ is a prime number, are groups. This paper aims to classify gyrogroups of orders 8, 12, 15, 18, 20, 21, and 28.},
keywords = {Gyrogroup,left Bol loop,gyroautomorphism},
url = {https://ajmc.aut.ac.ir/article_5063.html},
eprint = {https://ajmc.aut.ac.ir/article_5063_67d9057f7f7fb934e9000aefe2393820.pdf}
}