Some properties of Camina and $n$-Baer Lie algebras

Ghezelsoflo, Maryam; Moghaddam, Mohammad Reza Rajabzadeh; Rostamyari, Mohammad Amin; Saffarnia, Somayeh

doi:10.22103/jmmr.2024.23435.1648

تعداد نشریات	26
تعداد شماره‌ها	447
تعداد مقالات	4,557
تعداد مشاهده مقاله	5,380,003
تعداد دریافت فایل اصل مقاله	3,580,074

	Some properties of Camina and $n$-Baer Lie algebras
Journal of Mahani Mathematical Research
دوره 13، شماره 4 - شماره پیاپی 29، اسفند 2024، صفحه 153-164 اصل مقاله (486.67 K)
نوع مقاله: Special Issue Dedicated to Prof. Esfandiar Eslami
شناسه دیجیتال (DOI): 10.22103/jmmr.2024.23435.1648
نویسندگان
Maryam Ghezelsoflo¹؛ Mohammad Reza Rajabzadeh Moghaddam^* ²^{، 3}؛ Mohammad Amin Rostamyari²؛ Somayeh Saffarnia³
¹Department of Mathematics, Mashhad Branch Islamic Azad University, Mashhad, Iran
²Department of Mathematics, Khayyam University, Mashhad, Iran
³Department of Pure Mathematics, Centre of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, Mashhad, Iran
چکیده
Let $I$ be a non-zero proper ideal of a Lie algebra $L$. Then $(L, I)$ is called a Camina pair if $I \subseteq [x,L]$, for all $x \in L\setminus I$. Also, $L$ is called a Camina Lie algebra if $(L, L^2)$ is a Camina pair. We first give some properties of Camina Lie algebras, and then show that all Camina Lie algebras are soluble. Also, a new notion of $n$-Baer Lie algebras is introduced, and we investigate some of its properties, for $n=1, 2$. A Lie algebra $L$ is said to be $2$-Baer if for any one dimensional subalgebra $K$ of $L$, there exists an ideal $I$ of $L$ such that $K$ is an ideal of $I$. Finally, we study three classes of Lie algebras with $2$-subideal subalgebras and give some relations among them.
کلیدواژه‌ها
Camina Lie algebra؛ $n$-Baer Lie algebra؛ $2$-subideal subalgebra؛ nilpotent Lie algebra

مراجع
[1] Baer, R. (1993). Situation der Untergruppen und Struktur der Gruppen, Sitz. Heidelberg Akademie Wiss. Math.-Natur. Kl., 2, 12-17. [2] Camina, AR. (1978). Some conditions which almost characterize Frobenius groups, Israel J. Math., 31, 153-160. https://doi.org/10.1007/BF02760546. [3] Cangelmi, L., & Muktibodh, AS. (2010). Camina kernels with few conjugacy classes, Algebra Discrete Math., 9, 39-49. [4] Cappitt, D. (1971). Generalized Dedekind groups, J. Algebra, 17, 310-316. https://doi.org/10.1016/0021-8693(71)90013-5. [5] Cartan, E. (1984). Sur la structure des groupes de transformations nis et continus, Oevres Completes, 1, CNRS, 137-288. https://books.google.com/book?id=JY8LAAAAYAAJ&oe=UTF-8. [6] Chillag, D., & MacDonald, ID. (1984). Generalized Frobenius groups, Israel J. Math., 47, 111-122. https://doi.org/10.1007/BF02760510. [7] Chillag, D., Mann, A., & Scoppola, CM. (1988). Generalized Frobenius groups II, Israel J. Math., 62, 269-282. https://doi.org/10.1007/BF02783297. [8] Cicalo, S., de Graaf, WA., & Schneider, C. (2012). Six-dimensional nilpotent Lie algebras, Linear Algebra Appl., 436, 163-189. https://doi.org/10.1016/j.laa.2011.06.037. [9] Dark, R., & Scoppola, CM. (1996). On Camina groups of prime power order, J. Algebra, 181, 787-802. https://doi.org/10.1006/jabr.1996.0146. [10] Dedekind, R. (1897). Uber Gruppen, deren samtliche Teiler Normalteiler sind, Math. Ann., 48, 548-561. https://doi.org/10.1515/9783110208221.bm. [11] Kappe, LC., & Tortora, A. (2017). A generalization of 2-Baer groups, Comm. Algebra, Vol. 45, No. 9, 3994-4001. https://doi.org/10.1080/00927872.2016.1252385. [12] Herzog, M., Longobardi, P., & Maj, M. (2011). On in nite Camina groups, Comm. Algebra, 39, 4403-4419. https://doi.org/10.1080/00927872.2010.524684. [13] Isaacs, IM. (1989). Coprime group actions xing all nonlinear irreducible characters, Canad. J. Math., 41, 68-82. https://doi.org/10.4153/CJM-1989-003-2. [14] Lewis, ML. (2012). On p-group Camina Pairs, J. Group Theory, 15, 469-483. https://doi.org/10.1515/jgt-2012-0010. [15] Mahdavi, K. (1986). On groups with every subgroup 2-subnormal, Arch. Math. (Basel), 47(4), 289-292. https://doi.org/10.1007/BF01191351. [16] Muktibodh, AS., & Ghate, SH. (2013). On Camina group and its generalizations, Mat. Vesnik, 65, 250-260. [17] Sheikh-Mohseni, S., & Saeedi, F. (2018). Camina Lie algebras, Asian-Eur. J. Math., 11, No. 5, 1850063. https://doi.org/10.1142/S1793557118500638. [18] Roseblade, JE. (1965). On groups in which every subgroup is subnormal, J. Algebra, 2, 402-412. https://doi.org/10.1016/0021-8693(65)90002-5. [19] Wielandt, H. (1939). Eine Verallgemeinerung der invarianten Untergruppen, Math. Z., 45, 209-244. https://doi.org/10.1007/BF01580283.
آمار تعداد مشاهده مقاله: 88 تعداد دریافت فایل اصل مقاله: 66

سامانه مدیریت نشریات علمی. طراحی و پیاده سازی از سیناوب

پیوندهای مفید

آمار

Some properties of Camina and $n$-Baer Lie algebras