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Classification of gyrogroups of orders at most 31 | ||
| AUT Journal of Mathematics and Computing | ||
| مقاله 2، دوره 5، شماره 1، 2024، صفحه 11-18 اصل مقاله (362.08 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2023.21939.1125 | ||
| نویسندگان | ||
| Ali Reza Ashrafi1؛ Kurosh Mavaddat Nezhaad* 1؛ Mohammad Ali Salahshour2 | ||
| 1Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, Iran | ||
| 2Department of Mathematics, Savadkooh Branch, Islamic Azad University, Savadkooh, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Gyrogroup؛ Left Bol loop؛ Gyroautomorphism | ||
| مراجع | ||
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