Abstract
Given a sequence $$\{C_i\}_{i \in \mathbb N}$$ of cyclic groups of prime orders, let $$\Gamma _\infty $$ be the inverse limit of the iterated wreath products $$C_m \wr \cdots \wr C_2 \wr C_1$$ . We prove that the profinite group $$\Gamma _\infty $$ is not topologically finitely invariably generated.
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