非对称性Goursat引理的推广

On the generalization of asymmetry of Goursat's lemma

文章根据群与环上Goursat引理的非对称版本,得到了理想上的Goursat引理,并给出了计算3个三次交错群的直积的子群与Z_(2)×Z_(2)×Z_(2)的子环的一般步骤。另外,进一步考虑有限个群直积的一个子群K和任意子群G的积都有对应的Goursat分解下的性质,并给出了有限个环直积下的理想形式。

In this paper,according to the asymmetric version of Goursat's lemma on groups and rings,the Goursat's lemma on ideals is obtained,and the general steps for calculating the subgroups of the direct product of three cubic alternating groups and the rings of Z_(2)×Z_(2)×Z_(2) are given.In addition,the product of a subgroup K and any subgroup G of the direct product of finite groups'properties under the corresponding Goursat decomposition is considered,and the form of ideal under the direct product of a finite number of rings is given.