Mathematics – Group Theory
Scientific paper
2004-03-14
Mathematics
Group Theory
8 pages
Scientific paper
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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