Solution to the presentation problem for powers of the augmentation ideal of torsion free and torsion abelian groups
Solution to the presentation problem for powers of the augmentation ideal of torsion free and torsion abelian groups
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DOI：
10.1016/j.aim.2003.11.002
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发表时间：
2004-12
影响因子：
1.7
通讯作者：
A. Bak;G. Tang
中科院分区：
文献类型：
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作者：
A. Bak;G. Tang
本文利用Δn(G)的标准加法生成元解决了自由挠群和挠阿贝尔群G的整数群环ZG的增广理想Δ(G)的n次方Δn(G)的表示问题.当G本身有基且为扭时，得到了Δn(G)的一个具体基.这些结果被用于描述序列Δn(N)G↣Δn(G)↠Δn(G/N)的同调。
This paper solves for torsion free and torsion abelian groups G the problem of presenting nth powers Δn(G) of the augmentation ideal Δ(G) of an integral group ring Z G , in terms of the standard additive generators of Δn(G). A concrete basis for Δn(G) is obtained when G itself has a basis and is torsion. The results are applied to describe the homology of the sequence Δn(N)G↣Δn(G)↠Δn(G/N) .