p-可解群中子群的相互作用

The Action of Subgroups on p-solvable Groups

利用可解群的性质和有限群的基本定理,通过局部分析方法研究了p-可解群中一些子群的性质及子群间的相互作用,并着重考察了Op′(G)=1的情况,得到了关于p-可解群的一些结论.

The partly analytical method is the most basic one of finite groups. Using the properties of solva- ble groups and the basic theorems of finite groups, and utilizing the partly analytical method, the properties of some subgroups of p-solvable groups and the action on subgroups are studied. In this paper, the case of Op- （G） = 1 is especially considered, and some results of p - solvable groups are obtained.