群对其子群的相对同调

Relative homology of a group over its subgroups

提出了用群的轨道核来研究群同调的方法,并由此给出关于群同调的Mayer-vietors定理一个新的纯代数证明,进而引出群关于其子群的相对同调,证明了有关的性质及相应的同调谱序列。

The group homology by a new point of view of the 'kernel ornit' are studied. And then a new pure algebraic proof of Mayer-Vietors Theorem of group homology is given; Forthermore the relative homology of a group over its subgroups is defined and a homological spectral sequence of a series of subgroups is proved.