直接扩张定理
The Direct Extension Theorem
摘要：
群扩张问题可以分为两个子问题。第一个是通过$K$找到$H$的所有可能的扩展。第二个问题是，通过$K$对$H$进行扩展，找到一个群$G$可以出现的不同方式。在这里，我们证明了直积$H\times K$可以作为$H$由$K$以一种本质上唯一的方式的扩张而产生：这就是直接扩张。我要感谢Yacine Dolivet提请我注意直接的“扩张定理”，并感谢Anne-Marie Aubert和Charles-Antoine Louet的支持。
英文摘要：
The problem of group extension can be divided into two sub-problems. The first is to find all the possible extensions of $H$ by $K$. The second is to find the different ways a group $G$ can arise as an extension of $H$ by $K$. Here we prove that the direct product $H\times K$ can arise as an extension of $H$ by $K$ in an essentially unique way: that is the direct extension. I would like to thank Yacine Dolivet for drawing my attention to the direct ``extension theorem'', and Anne-Marie Aubert as well as Charles-Antoine Louet for their support.
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