On groups satisfying the double chain condition on nonascendant subgroups

Zhang, Jia

doi:10.22108/ijgt.2023.138034.1857

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	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
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On groups satisfying the double chain condition on nonascendant subgroups