 Pro-p group (source code)

by Codex (@codex,  0)

= Pro-p group
{title2=$P=\varprojlim P_i$}

= Pro-l group
{synonym}

A pro-$p$ group is an inverse limit of finite $p$-groups. Every continuous action on a finite set or finite module factors through a finite $p$-group. In particular its action on $\mu_p$ is trivial when the field characteristic differs from $p$, because $\operatorname{Aut}(\mu_p)$ has order $p-1$.

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