In this paper, we study the basis of augmentation ideals and the quotient groups of finite non-abelian p-group which has a cyclic subgroup of index p, where p is an odd prime, and k is greater than or equal to 3. A co...In this paper, we study the basis of augmentation ideals and the quotient groups of finite non-abelian p-group which has a cyclic subgroup of index p, where p is an odd prime, and k is greater than or equal to 3. A concrete basis for the augmentation ideal is obtained and then the structure of its quotient groups can be determined.展开更多
In this article we describe the stable behavior of the augmentation quotients Qn （G） for the groups G of order p^5 with even numbers of generators, where p is an odd prime.
Let G be a finite abelian group and its Sylow p-subgroup a direct product of copies of a cyclic group of order p<sup>r</sup>,i.e.,a finite homocyclic abelian group.LetΔ<sup>n</sup> （G） denot...Let G be a finite abelian group and its Sylow p-subgroup a direct product of copies of a cyclic group of order p<sup>r</sup>,i.e.,a finite homocyclic abelian group.LetΔ<sup>n</sup> （G） denote the n-th power of the augmentation idealΔ（G） of the integral group ring ZG.The paper gives an explicit structure of the consecutive quotient group Q<sub>n</sub>（G）=Δ<sup>n</sup>（G）/Δ<sup>n+1</sup>（G） for any natural number n and as a consequence settles a problem of Karpilovsky for this particular class of finite abelian groups.展开更多
文摘In this paper, we study the basis of augmentation ideals and the quotient groups of finite non-abelian p-group which has a cyclic subgroup of index p, where p is an odd prime, and k is greater than or equal to 3. A concrete basis for the augmentation ideal is obtained and then the structure of its quotient groups can be determined.
文摘In this article we describe the stable behavior of the augmentation quotients Qn （G） for the groups G of order p^5 with even numbers of generators, where p is an odd prime.
基金This work was supported by the National Natural Science Foundation of China (Grant No.10271094)"Hundred Talent"Program of the Chinese Academy of Sciences
文摘Let G be a finite abelian group and its Sylow p-subgroup a direct product of copies of a cyclic group of order p<sup>r</sup>,i.e.,a finite homocyclic abelian group.LetΔ<sup>n</sup> （G） denote the n-th power of the augmentation idealΔ（G） of the integral group ring ZG.The paper gives an explicit structure of the consecutive quotient group Q<sub>n</sub>（G）=Δ<sup>n</sup>（G）/Δ<sup>n+1</sup>（G） for any natural number n and as a consequence settles a problem of Karpilovsky for this particular class of finite abelian groups.
文摘令 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.
基金The research was supported by the National Natural Science Foundation of China(11461010)the Guangxi Science Research and Technology Development Project(1599005-2-13)the Scientific Research Fund of Guangxi Education Department(KY2015ZD075)
