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Some properties of finite generalized-groups | ||
| Journal of Mahani Mathematical Research | ||
| دوره 13، شماره 4 - شماره پیاپی 29، اسفند 2024، صفحه 101-107 اصل مقاله (430.26 K) | ||
| نوع مقاله: Special Issue Dedicated to Prof. Esfandiar Eslami | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2024.23326.1625 | ||
| نویسنده | ||
| Nosratollah Shajareh Poursalavati* 1، 2 | ||
| 1Department of Pure Mathematics , Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran | ||
| 2Mahani Math Center, Afzalipour Research Institute, Shahid Bahonar University of Kerman, Kerman, Iran | ||
| چکیده | ||
| In this article, we discuss the concept of completely simple-semigroups, which serves as a natural extension of the group structures. These semigroups, also known as generalized-groups, provide an interesting generalization beyond the realm of the groups. Many scientists have investigated various applications of generalized-groups. Notably, this algebraic structure has connections to the unified gauge theory. In this article, we investigate the structures and properties of generalized-groups, providing examples and results within this fascinating subject. Specially, we show that the generalized Lagrange Theorem may not be true for generalized-groups. | ||
| کلیدواژه‌ها | ||
| Completely simple semigroups؛ Groups؛ Generalized-groups؛ Algebraic structure | ||
| مراجع | ||
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[2] Agboola, A. A. A. (2004). Certain properties of generalized-groups. Proc. Jangjeon Math. Soc., 7(2), 137-148.
[3] Ahmadi Zand, M. R., & Rostami, S. (2016). Precompact topological generalized-groups. J. Mahani Math. Res. Cent., 5(1-2) 27-32. https://doi.org/10.22103/jmmrc.2017.1565
[4] Akinmoyewa, J. T. (2009). A study of some properties of generalized-groups. Octogon Mathematical Magazine, 17(2), 599-626.
[5] Araujo, J., & Konieczny, J. (2002). Molaei's generalized-groups are completely simple semigroups. Buletinul Institului Polithnic Din Iasi., 48, 1-5.
[6] Molaei, M. R. (1998). Generalized groups. Proceeding of the International Conference on Algebra, October 14-17, Romania.
[7] Molaei, M. R. (1999). Generalized actions. In Geometry, integrability and quantization, (Varna), 175-179.
[8] Romeo, P. G., & Sneha, K. K. (2020). Generalized groups and module groupoids. arXiv:2010.05756v1 [math.GM] 9 Oct 2020.
[9] Smith, J. D. H. (2007). An Introduction to Quasigroups and their Representations. CRC Press. ISBN 978-1-58488-537-5.
[10] Vagner, V. V. (1952). Generalized groups. Doklady Akad. Nauk SSSR (N.S.), 84, 1119-1122. | ||
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