%0 Journal Article
%T Classification of gyrogroups of orders at most 31
%J AUT Journal of Mathematics and Computing
%I Amirkabir University of Technology
%Z 2783-2449
%A Ashrafi, Ali Reza
%A Mavaddat Nezhaad, Kurosh
%A Salahshour, Mohammad Ali
%D 2024
%\ 01/01/2024
%V 5
%N 1
%P 11-18
%! Classification of gyrogroups of orders at most 31
%K Gyrogroup
%K left Bol loop
%K gyroautomorphism
%R 10.22060/ajmc.2023.21939.1125
%X 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.
%U https://ajmc.aut.ac.ir/article_5063_67d9057f7f7fb934e9000aefe2393820.pdf