论文标题
关于有限$ t $ -groups的概括
On a generalisation of finite $T$-groups
论文作者
论文摘要
令$σ= \ {σ_i| i \ in I \} $是所有Primes $ \ mathbb {p} $和$ g $的某些分区。如果存在一个子组链$ h = h_1 \ leq h_1 \ leq \ cdots \ cdots \ leq h_n = g $，则$ g $的亚组$ h $ of $ g $在$ g $中为$σ$ -subnormal in $ g $。有限$σ_j$ -group，用于$ i = 1，\ ldots，n $的$ j \ in i $ in in $ j \。如果每个$σ$ -Subnormal子组在$ g $中是正常的，我们将称为有限组$ g $ a $t_σ$ -group。在本文中，我们分析了$t_σ$ groups的结构，并给出了$t_σ$ groups的一些特征。
Let $σ=\{σ_i |i\in I\}$ is some partition of all primes $\mathbb{P}$ and $G$ a finite group. A subgroup $H$ of $G$ is said to be $σ$-subnormal in $G$ if there exists a subgroup chain $H=H_0\leq H_1\leq \cdots \leq H_n=G$ such that either $H_{i-1}$ is normal in $H_i$ or $H_i/(H_{i-1})_{H_i}$ is a finite $σ_j$-group for some $j \in I$ for $i = 1, \ldots, n$. We call a finite group $G$ a $T_σ$-group if every $σ$-subnormal subgroup is normal in $G$. In this paper, we analyse the structure of the $T_σ$-groups and give some characterisations of the $T_σ$-groups.
