TY - JOUR
ID - 5063
TI - Classification of gyrogroups of orders at most 31
JO - AUT Journal of Mathematics and Computing
JA - AJMC
LA - en
SN - 2783-2449
AU - Ashrafi, Ali Reza
AU - Mavaddat Nezhaad, Kurosh
AU - Salahshour, Mohammad Ali
AD - Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, Iran
AD - Department of Mathematics, Savadkooh Branch, Islamic Azad University, Savadkooh, Iran
Y1 - 2024
PY - 2024
VL - 5
IS - 1
SP - 11
EP - 18
KW - Gyrogroup
KW - left Bol loop
KW - gyroautomorphism
DO - 10.22060/ajmc.2023.21939.1125
N2 - 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.
UR - https://ajmc.aut.ac.ir/article_5063.html
L1 - https://ajmc.aut.ac.ir/article_5063_67d9057f7f7fb934e9000aefe2393820.pdf
ER -