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

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 .