I'm seeking for some nice examples for powerful pro-p-groups* for prime $p \neq 2$.
By definition a powerful $p$- group $G$ is definined by following property: The commutator $[G,G]$ is contained in $ G^p = ⟨ g^p | g ∈ G ⟩ $.
For pro-$p$ case $G$ is endowed with pro-$p$-topology, so we have following modified condition:
$[G,G] \subset \overline{G^p} $.
