有限群的π-弱拟正规子群Ⅰ（英）

引进π-拟正规性的推广概念π-弱拟正规性.有限群G的子群K称为在G中π-弱拟正规,若K同G的每个Sylow π-子群可换.探讨了π-弱拟正规子群的一些性质,给出了一些实例和实事,比较详细地比较了有限群的π-拟正规子群和π-弱拟正规子群,说明π-弱拟正规子群概念是π-拟正规子群概念的真正推广,得到了极大子群皆π-弱拟正规的有限群类的分类定理.

π-Weak Quasinormal Subgroups of Finite Groups Ⅰ

In this paper, as a generalization of quasinormality, the concept of π-weak quasinormality is introduced. Some properties of π-weak quasinormal subgroups are studied. A classification theorem of the class of finite groups with maximal subgroups which are π-weak quasinormal is obtained.