The Direct Extension Theorem
Joseph, Ayoub
Original · EN
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× 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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