群中心扩张与二维上同调群通用系数定理

CENTRAL EXTENSIONS OF A GROUP AND THE UNIVERSAL COEFFICIENT THEOREM IN THE COHOMOLOGY GROUPS OF DIMENSION 2

本文在Ｇｒｕｅｎｂｅｒｇ［３］中给出的范畴（Ｔｒ｜｜Ｇ）之中心自由对象构作基础上进行群Ｇ的中心扩张构作，使用了覆盖图及行生同态Ｅ０为中心自由扩张，文中称作普适覆盖扩张，Ｅ是Ａｂｅｌ群Ａ经群Ｇ的中心扩张。定理１指出是一个二因子次直接和，尽管非交换，因子之一为Ｖ经Ｈ１（Ｇ）的交换扩张，另一是Ｇ的本盖扩张，二者上交于因子群Ｈ１（Ｇ）．再用定理１得到二维上同调群通用系数定理的一个另一种证明．余下是普适覆盖扩张的构作。

In according with the constrUction of central free objects in Category(Tr||G)givenby Gruenberg in [3], this article deals with the construction and equivalent classificationof central extensions of a group G, making use of generating homomorphisms 9,which occur in the covering diagrams as followsThe exact sequence E0 is a central free extension, which is called a universally coveringextension in our work, and E is a central extension of abelian group A by, group G.Theorem 1 asserts that g is a subdirect sum of two factors, though to be non- commutative. The one is a conunutative extension of V by HI(G), and the other is a stemcover of G. Both cointersect at the common factor group H,(G). Utilizing Theorem1, an alternative proof of the universal coefficient theorem in cohpmology groups of2-dimension is obtained with ease. The remaining book' is: to reduce the constructionof universally covering extensions, having got tWo adultS ti be if s'ignificance.