On groups satisfying the double chain condition on nonascendant subgroups

Zhang, Jia

doi:10.22108/ijgt.2023.138034.1857

تعداد نشریات	42
تعداد شماره‌ها	1,537
تعداد مقالات	12,623
تعداد مشاهده مقاله	25,831,296
تعداد دریافت فایل اصل مقاله	10,662,307

	On groups satisfying the double chain condition on nonascendant subgroups
International Journal of Group Theory
مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 07 مهر 1402 اصل مقاله (370.09 K)
نوع مقاله: Ischia Group Theory 2022
شناسه دیجیتال (DOI): 10.22108/ijgt.2023.138034.1857
نویسنده
Jia Zhang^*
Pingxiang Universiry
چکیده
If $\theta$ is a subgroup property, a group $G$ is said to satisfy the double chain condition on $\theta$-subgroups if it admits no infinite double chain $$\cdots<X_{-n}<\cdots<X_{-1}<X_0<X_1<\cdots<X_n<\cdots$$ consisting of $\theta$-subgroups. Here we want to describe the structure of locally finite and locally nilpotent groups satisfying the double chain condition on non-ascendant subgroups in term of chain conditions and of ascendant subgroups.
کلیدواژه‌ها
Double chains؛ ascendant subgroups؛ locally finite groups؛ locally nilpotent groups

مراجع
[1] M. Brescia, Groups satisfying the double chain condition on non-subnormal subgroups, J. Group Theory, 24 (2021) 95–108. [2] M. Brescia, F C-groups with few subnormal non-normal subgroups, Mediterr. J. Math., 19 (2022) 19 pp. [3] M. Brescia and F. de Giovanni, Groups satisfying the double chain condition on subnormal subgroups, Ric. Mat., 65 (2016) 255–261. [4] M. Brescia and F. de Giovanni, Groups satisfying the double chain condition on non-pronormal subgroups, Riv. Mat. Univ. Parma, 8 (2017) 353–366. [5] M. Brescia and F. de Giovanni, Groups satisfying the double chain condition on subnormal non-normal subgroups, Adv. Group Theory Appl., 13 (2022) 83–102. [6] M. Brescia and A. Russo, Groups satisfying the double chain condition on abelian subgroups, Bull. Aust. Math. Soc., 99 (2019) 212–218. [7] M. Brescia and A. Russo, Groups satisfying the double chain condition on non-abelian subgroups, J. Algebra Appl., 19 (2020) 14 pp. [8] S. N. Chernikov, Infinite locally soluble groups, Mat. Sb., 7 (1940) 35–64. [9] K. A. Hirsch, On infinite soluble groups I, Proc. London Math. Soc. (2), 44 (1938) 53–60. [Malcev(1951)] A. I. Malcev, On certain classes of infinite soluble groups, Mat. Sb., 28 (1951) 567–588. [10] B. I. Plotkin, On groups with finiteness conditions for abelian subgroups, Dokl. Akad. Nauk. SSSR, 107 (1956) 648–651. [11] D. Robinson, Finiteness Conditions and Generalized Soluble Groups, Springer, Berlin, 1972. [12] D. Robinson, A Course in the Theory of Groups, Springer, Berlin, 1982. [13] O. J. Schmidt, Infinite soluble groups, Mat. Sb., 17 (1945) 145–162. [14] T. S. Shores, A chain condition for groups, Rocky Mountain J. Math., 3 (1973) 83–89. [15] V. P. Šunkov, On locally finite groups with a minimality conditions for abelian subgroups,Algebra and Logic, 10 (1971) 199–225. [16] D. I. Zaicev, On solvable subgroups of locally solvable groups, Soviet Math. Dokl., 15 (1974) 342–345.
آمار تعداد مشاهده مقاله: 9 تعداد دریافت فایل اصل مقاله: 9

سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب

پیوندهای مفید

اخبار و اعلانات

آمار

On groups satisfying the double chain condition on nonascendant subgroups