A generalization of $c$-Supplementation

Alperin融合定理的推广及其应用

A generalization of Alperin fusion theorem and its applications

本文推广了Alperin融合定理，引入关于强闭子群的本质子群概念，证明了分解定理与正规性准则，并发展了拟饱和与半饱和融合系统理论。

A generalization of Sims conjecture for finite primitive groups and two point stabilizers in primitive groups

In this paper we propose a refinement of Sims conjecture concerning the cardinality of the point stabilizers in finite primitive groups and we make some progress towards this refinement. In this process, when dealing with primitive groups of diagonal type, we construct a finite primitive group $G$ on $Ω$ and two distinct points $α,β\in Ω$ with $G_{αβ}\unlhd G_α$ and $G_{αβ}\ne 1$, where $G_α$ is the stabilizer of $α$ in $G$ and $G_{αβ}$ is the stabilizer of $α$ and $β$ in $G$. In particular, this example gives an answer to a question raised independently by Peter Cameron and by Alexander Fomin…