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
مقاله 2، دوره 14، شماره 1، خرداد 2025، صفحه 1-7 اصل مقاله (382.48 K)
نوع مقاله: Ischia Group Theory 2022
شناسه دیجیتال (DOI): 10.22108/ijgt.2023.138034.1857
نویسنده
Jia Zhang^*
Pingxiang Universiry, Pingxiang, China
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