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On autocentral kernel of groups | ||
| Journal of Mahani Mathematical Research | ||
| دوره 14، شماره 2 - شماره پیاپی 32، مرداد 2025، صفحه 343-352 اصل مقاله (482.16 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2025.24620.1745 | ||
| نویسندگان | ||
| Shafigh Bahri؛ Azam Kaheni* ؛ Mohammad Mehdi Nasrabadi | ||
| Department of Mathematics, University of Birjand, Birjand, Iran | ||
| چکیده | ||
| Let $G$ be a group, where $\text{Aut}(G)$ denotes the full automorphisms group of $G$ and $L(G)$ represents the absolute center of $G.$ An automorphism $\alpha \in \text{Aut}(G)$ is called an autocentral automorphism if $g^{-1}\alpha(g) \in L(G),$ for all $g \in G .$ In this paper, we introduce the notion of autocentral kernel subgroup for an arbitrary group $G.$ We then investigate and establish several structural properties of this subgroup, providing insights into its role within the broader framework of group theory. | ||
| کلیدواژه‌ها | ||
| Absolute central automorphisms؛ Absolute centre؛ Autocentral kernel؛ Autonilpotent group | ||
| مراجع | ||
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[7] Moghaddam, M. R. R., & Safa, H. (2010). Some properties of autocentral automorphisms of a group. Ric. Mat, 59, 257{264. https://doi.org/10.1007/s11587-010-0085-6
[8] Nasrabadi, M.M., & Kaboutari Farimani, Z. (2015). Absolute central automorphisms that are inner. Indagationes Mathematicae, 26, 137{141. https://doi.org/10.1016/j.indag.2014.08.003
[9] Or , R., & Fouladi, S. (2020). The Absolute Center of p-Groups of Maximal Class. Filomat 34(13), 4483{4487. https://doi.org/10.2298/FIL2013483O
[10] Parvaneh, F. (2015). Some properties of autonilpotent groups. Italian Jornal of Pure and Applied Mathematics, 35 ,1-8.
[11] Robinson, D. J. S. (1996). A Course in the Theory of Groups. 2nd ed. Springer-verlag;New York, Heidelberg, Berlin. https://link.springer.com/book/10.1007/978-1-4419-8594-1 [12] Soleimani, R. (2022). A Note on Absolute Central Automorphisms of Finite p-Groups. Iranian Journal of Mathematical Sciences and Informatics,17(2 ), 97-108. https://doi.org/10.52547/ijmsi.17.2.97 | ||
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