一类非交换p-群的正规子群的补  

Complemented Subgroups of Normal Subgroups of Some Class of Nonabelian p-groups

作　　者：周芳[1] ZHOU Fang(Department of Mathematics,Taiyuan Normal University,Jinzhong Shanxi 030619,China)

机构地区：[1]太原师范学院数学系,山西晋中030619

出　　处：《忻州师范学院学报》2022年第2期9-10,37,共3页Journal of Xinzhou Teachers University

基　　金：太原师范学院研究生教育教学研究课题(SYYJSJG-2120)。

摘　　要：针对有限群G的正规子群的补子群的存在性问题,Schur-Zassenhaus定理从群的阶的角度给出了补子群存在的充分条件以及所有补子群之间的关系;在群作用的环境下Frattini论断给出了正规子群的补子群存在的充分条件。在此基础上,计算了一类非交换p^(n+1)(p≠2,n≥2)阶群的正规子群的补子群的结构,做为应用,给出了p^(3)阶非交换p-群的补子群存在的充分条件。On the existence of complemented subgroups of normal subgroups of finite group G,Schur-zassenhaus theorem gives sufficient conditions for the existence of complement subgroups of normal subgroups, and the relations among all complement subgroups.Frattini’s statement gives sufficient conditions for the existence of complement subgroups of normal subgroups in the context of group action.On this basis, the structure of the complement subgroups of normal subgroups of a class of nonabelian groups of order p^(n+1)(p≠2,n≥2) is calculated.As an application, the sufficient conditions for the existence of the complement subgroups of nonabelian p-groups of order p^(3) are given.

关 键 词：有限群 正规子群 补子群 非交换p-群 

分 类 号：O152.1[理学—数学]