某类群之增广理想及其增广商群的基底(英文)

Basis of powers of augmentation ideals and their quotient groups for some groups

令 H 是任意非 Abel 有限群G 的完全正规子群,记 ( )? n G为整群环 Z G的 n 次增广理想,( )Qn G 为增广商群 ( ) ( )? n G ? n+1G. 当 G H 为循环群或基本 p ? 群时,给出了 ( )? n G的一组基底,确定其增广商群 ( )Qn G 的结构.

Let G be a finite nonabelian group with a perfect normal subgroup H , let ( )? n G denote the n 'th power of the augmentation ideal ? ( G) of the integral group ring Z G and ( )Qn G the quotient group ( ) ( )? n G ? n+1G. When G H is a cyclic or an elementary p ? group, an explicit basis for ( )? n G is given and the structure of the quotient groups ( )Qn G is determined.