一类非阿贝尔p-群的整群环之增广商群的结构  

A note on the structure of the augmentation quotient group for some non-abelian p-groups

作　　者：王秀兰 周庆霞[2] WANG Xiulan;ZHOU Qingxia(College of Basic Science,Tianjin Agricultural University,Tianjin 300384,China;College of Science,Tianjin University of Technology,Tianjin 300384,China)

机构地区：[1]天津农学院基础科学学院,天津300384 [2]天津理工大学理学院,天津300384

出　　处：《湖北大学学报（自然科学版）》2019年第5期459-462,共4页Journal of Hubei University：Natural Science

摘　　要：令G是一个阶为p k的有限非阿贝尔p群且包含一个指数为p的循环子群,其中p≠2,k≥3.文献[1]中给出了这类群的整群环的增广理想的一组基底和增广商群的结构,但并不完全正确.笔者将沿用文献[1]中方法,给出这类群的整群环的增广理想正确的基底和其增广商群正确的结构.Let G be a finite non-abelian p -group of order p k with a cyclic subgroup of index p ,where p ≠2, k ≥3. The authors in[1] had given a basis of n -th augmentation ideal and the structure of n -th augmentation quotient group for the group G , but it is not very exact. In our research, following their method in[1], we construct an exact basis of n -th augmentation ideal and the structure of n -th augmentation quotient group for the group G .

关 键 词：整群环 增广理想 增广商群 P-群 

分 类 号：O153.3[理学—数学]