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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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[1] A. A. Albert, Quasigroups. I, Trans. Amer. Math. Soc., 54 (1943), pp. 507–519.
[2] , Quasigroups. II, Trans. Amer. Math. Soc., 55 (1944), pp. 401–419.
[3] R. Baer, Nets and groups, Trans. Amer. Math. Soc., 46 (1939), pp. 110–141.
[4] R. H. Bruck, Contributions to the theory of loops, Trans. Amer. Math. Soc., 60 (1946), pp. 245–354. [5] R. P. Burn, Finite Bol loops, Math. Proc. Cambridge Philos. Soc., 84 (1978), pp. 377–385.
[6] , Finite Bol loops. II, Math. Proc. Cambridge Philos. Soc., 89 (1981), pp. 445–455.
[7] , Corrigenda: “Finite Bol loops, III”, Math. Proc. Cambridge Philos. Soc., 98 (1985), pp. 381.
[8] , Finite Bol loops. III, Math. Proc. Cambridge Philos. Soc., 97 (1985), pp. 219–223.
[9] The GAP Group, GAP – Groups, Algorithms, and Programming, Version 4.11.1, 2021. https://www. gap-system.org.
[10] M. K. Kinyon, G. P. Nagy, and P. Vojtechovsk ˇ y´, Bol loops and Bruck loops of order pq, J. Algebra, 473 (2017), pp. 481–512.
[11] S. Mahdavi, A. Ashrafi, and M. Salahshour, Construction of new gyrogroups and the structure of their subgyrogroups, Algebr. Struct. their Appl., 8 (2021), pp. 17–30.
[12] G. E. Moorhouse, Bol loops of small order, 2007. https://ericmoorhouse.org/pub/bol/.
[13] G. P. Nagy and P. Vojtechovsk ˇ y´, The moufang loops of order 64 and 81, J. Symb. Comput., 42 (2007), pp. 871–883.
[14] H. Niederreiter and K. H. Robinson, Bol loops of order pq, Math. Proc. Cambridge Philos. Soc., 89 (1981), pp. 241–256.
[15] R. Penrose, Einstein’s Miraculous Year: Five Papers That Changed the Face of Physics, Princeton University Press, 2005.
[16] L. V. Sabinin, L. L. Sabinina, and L. V. Sbitneva, On the notion of gyrogroup, Aequationes Math., 56 (1998), pp. 11–17.
[17] T. Suksumran, The algebra of gyrogroups: Cayley’s theorem, Lagrange’s theorem, and isomorphism theorems, in Essays in mathematics and its applications, Springer, [Cham], 2016, pp. 369–437.
[18] , Special subgroups of gyrogroups: Commutators, nuclei and radical, Math. Interdisc. Appl., 1 (2016), pp. 53–68.
[19] A. A. Ungar, Thomas rotation and the parametrization of the Lorentz transformation group, Found. Phys. Lett., 1 (1988), pp. 57–89.
[20] , The Thomas rotation formalism underlying a nonassociative group structure for relativistic velocities, Appl. Math. Lett., 1 (1988), pp. 403–405.
[21] , The relativistic noncommutative nonassociative group of velocities and the Thomas rotation, Results Math., 16 (1989), pp. 168–179.
[22] A. A. Ungar, Analytic hyperbolic geometry and Albert Einstein’s special theory of relativity, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2008.
[23] , A gyrovector space approach to hyperbolic geometry, vol. 4 of Synthesis Lectures on Mathematics and Statistics, Morgan & Claypool Publishers, Williston, VT, 2009. | ||
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