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4.40 (1973)

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Let $C$ be a fixed non-trivial group (for instance, $C = \mathbb{Z}/2\mathbb{Z}$). As it is shown in (Yu. I. Merzlyakov, Algebra and Logic, 9, no. 5 (1970), 326–337), for any two groups $A$ and $B$, all split extensions of $B$ by $A$ can be imbedded in a certain unified way into the direct product $A \times \operatorname{Aut} (B \wr C)$. How are they situated in it?

Contributor: Yu. I. Merzlyakov

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