极小子群的S-正规性对有限群构造的影响

The influence of S-normality of minimal subgroups on the structure of finite groups

设G为有限群,极小子群在有限群的研究中扮演着一个十分重要的角色.利用极小子群的S-正规性刻划群G的结构,得到一个群p-幂零、幂零的一些充分条件,并推广了一些已知的结果.

Let G be a finite group. The minimal subgroups play an important role in the study of finite groups. In this paper, the S-normality of minimal subgroups are used to characterize the structure of the group G, some sufficent conditions are obtained under which a group belongs to p-nilpotent groups and nilpotent groups, and generalize some known results as well.