有限群的非Frattini主因子中$\mathrm{PSL}(2,p)$的识别

关于李代数的可补非交换主因子

On complemented non-abelian chief factors of a Lie algebra

由\cite [定理2.3]{[11]}证明了有限维李代数$L$的Frattini主因子或由极大子代数补的主因子的个数在$L$的每个主级数中是相同的。然而，对于在$L$中被简单补的主因子的数目，情况并非如此。在本文中，我们确定了这个数字的可能变化。

李代数的极大子代数与主因子

Maximal subalgebras and chief factors of Lie algebras

本文继续研究李代数的结构与它们的主因子的关系，所用的概念类似于群论中相应的概念。第一节研究了极大子代数无核的李代数的结构。第二节利用所得结果讨论了L的两个主因子是L-连通的关系，这是主因子集上的一种比同构为L-模的关系更弱的等价关系。Jordan-H的加强型对每一个李代数建立了Frattini主因子对应的Older定理。最后一节介绍了冠的概念，一个由Gasch在群论中引入的概念utz，并表明，它提供了许多信息的主要因素

Finite groups, minimal bases and the intersection number

Let $G$ be a finite group and recall that the Frattini subgroup ${\rm Frat}(G)$ is the intersection of all the maximal subgroups of $G$. In this paper, we investigate the intersection number of $G$, denoted $α(G)$, which is the minimal number of maximal subgroups whose intersection coincides with ${\rm Frat}(G)$. In earlier work, we studied $α(G)$ in the special case where $G$ is simple and here we extend the analysis to almost simple groups. In particular, we prove that $α(G) \leqslant 4$ for every almost simple group $G$, which is best possible. We also establish new results on the intersect…