Structure of finite groups with some weakly $S$-semipermutable subgroups

Jafarian Dehkordi, Hassan; Rezaeezadeh, Gholamreza; Bibak, Masoumeh

doi:10.22103/jmmr.2023.20941.1395

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	Structure of finite groups with some weakly $S$-semipermutable subgroups
Journal of Mahani Mathematical Research
دوره 13، شماره 1 - شماره پیاپی 26، بهمن 2023، صفحه 457-466 اصل مقاله (489.34 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22103/jmmr.2023.20941.1395
نویسندگان
Hassan Jafarian Dehkordi^* ¹؛ Gholamreza Rezaeezadeh²؛ Masoumeh Bibak³
¹Department of Mathematics, payme Noor University, P. O. Box 19395-4697, Tehran, IRAN
²Faculty of Mathematical Sciences, University of Shahrekord, Shahrekord, Iran.
³Department of Mathematics, University of Payme Noor, P.O.Box 19395-4697, Tehran, Iran
چکیده
Let $ G $ be a finite group. If $ A\leq G $, recall that $ A $ is weakly $S$-semipermutable in $G$ provided there is $K\unlhd G$ such that $KA$ is $S$-permutable in $G$, and $K\cap A$ is $S$-semipermutable in $G$. The purpose of this paper is to demonstrate that weakly $S$-semipermutability of special types of subgroups in a finite group $ G $ can help us to determine structural properties of $ G $. For example, given a prime $p$, a $p$-soluble finite group $G$ and a Sylow $p$-subgroup $G_{p}$ of $G$, we will show that $G$ is $p$-supersoluble if the maximal subgroups of $G_{p}$ are weakly $S$-semipermutable in $ G$. Moreover, we use the concept of weakly $S$-semipermutability to prove new criteria for $p$-nilpotency of finite groups.
کلیدواژه‌ها
p-nilpotent؛ p-supersoluble؛ weakly S-semipermutable

مراجع
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Structure of finite groups with some weakly $S$-semipermutable subgroups