非正规子群共轭类数为p+2的有限p群的分类  

The Classification of Finite p -group with p+2 Conjugacy Classesof Non-normal Subgroups

作　　者：张慧玲[1] ZHANG Huiling(Taiyuan University,Taiyuan 030001,China)

机构地区：[1]太原学院数学系,太原030001

出　　处：《太原师范学院学报（自然科学版）》2023年第2期8-12,23,共6页Journal of Taiyuan Normal University:Natural Science Edition

基　　金：教学改革创新项目(J20221220)。

摘　　要：利用非正规子群的共轭类研究有限p群的结构是有限p群领域一个重要的研究内容,其中p表示一个素数.对于非正规子群共轭类数为p+2的有限p群,按照导群的阶分p和p^(2)两种情况进行讨论,利用中心积和中心扩张的方法,给出了非正规子群共轭类数为p+2的有限p群的具体分类.It is an important research in the field of finite p-groups to study the structure of finite p-groups by using the conjugate classes of non-normal subgroups,where p denotes a prime number.For finite p-group with p+2 conjugate classes of non-normal subgroups,the method of central product and central extension is discussedand where the order of the derived group is equal to p and p^(2),the concrete classification of finite p-group with p+2 conjugate classes of non-normal subgroups is given.

关 键 词：有限P群 非正规子群 共轭类数 

分 类 号：O152.1[理学—数学]