相对同调的等价刻划及相对欧拉示性数

An Equivalent Description of the Relative Homology and Relative Euler Characteristic

给出群关于其子群的相对同调的一个等价刻划。并把群的欧拉示性数推广到相对同调群上去，证明了群关其子群的相对欧拉示性数等于干群的欧拉示性数减去大群的欧拉示性数．

In this paper, an equivalent description of the relative homology is given. And, theconcept of Euler characteristics of groups is generalized into the case of relative homology. It isproved that the relative Euler characteristic of group over its subgroup is equal to the Eulercharacteristic of the subgroup minus the Euler characteristic of the group.