Powerfully embedded subgroup
= Powerfully embedded subgroup
{title2=$[N,G]\leq N^p$}
= Powerfully embedded
{synonym}
A <normal subgroup> $N$ is powerfully embedded in a <finite p-group> or <pro-p group> $G$ if $[N,G]\leq N^p$ for odd $p$, or $[N,G]\leq N^4$ for $p=2$; use closed generated <subgroups> in the <pro-p group> case. The condition implies that $N$ is a <powerful p-group>. For odd $p$, both $[N,G]$ and $N^p$ remain powerfully embedded.