تقرير
A contribution to the theory of $\sigma$-properties of a finite group
| العنوان: | A contribution to the theory of $\sigma$-properties of a finite group |
|---|---|
| المؤلفون: | Liu, A-Ming, Guo, Wenbin, Safonov, Vasily G., Skiba, Alexander N. |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Group Theory, 20D10, 20D15, 20D30 |
| الوصف: | We characterize some classes of finite soluble groups. In particular, we prove that: a finite group $G$ is supersoluble if and only if $G$ has a normal subgroup $D$ such that $G/D$ is supersoluble and $D$ avoids every chief factor of $G$ between $V^{G}$ and $V_{G}$ for every maximal subgroup $V$ of the generalized Fitting subgroup $F^{*}(G)$ of $G$; a finite soluble group $G$ is a $PST$-group (that is, Sylow permutability is a transitive relation on $G$) if and only if $G$ has a normal subgroup $D$ such that $G/D$ is nilpotent and $D$ avoids every chief factor of $G$ between $V^{G}$ and $V_{G}$ for every subnormal subgroup $A$ of $G$. Comment: 19 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2404.00004 |
| رقم الأكسشن: | edsarx.2404.00004 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |