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The Krasner–Kaloujnine universal embedding theorem states that any group extension of a group $H$ by a group $A$ is isomorphic to a subgroup of the regular wreath product $A \operatorname{Wr} H$. When ...

I am currently looking for a reference to a proof (or counterexample) to the following statement: Statement: Assume $G$ is a finitely generated solvable group of exponential growth, then there is a ...