Powerful pro-p group
= Powerful pro-p group
{title2=$[G,G]\subseteq G^{p^\epsilon}$}
A <pro-p group> whose closed <commutator subgroup> lies in its closed power subgroup $G^{p^\epsilon}$, with $\epsilon=1$ for odd $p$ and $\epsilon=2$ for $p=2$. This is the profinite analogue of a <powerful p-group>. Finitely generated torsion-free examples are exactly the <uniform pro-p groups>. The additive <group> of a finite product of <p-adic integers> is an abelian example.