On automorphisms of free pro-𝑝-groups. I

Herfort, Wolfgang N.; Ribes, Luis

doi:10.1090/S0002-9939-1990-0984794-6

On automorphisms of free pro-$p$-groups. I
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by Wolfgang N. Herfort and Luis Ribes PDF

Proc. Amer. Math. Soc. 108 (1990), 287-295 Request permission

Abstract:

Let $F$ be a (topologically) finitely generated free pro-$p$-group, and $\beta$ an automorphism of $F$. If $p \ne 2$ and the order of $\beta$ is 2, then there is some basis of $F$ such that $\beta$ either fixes or inverts its elements. If $p$ does not divide the order of $\beta$, then the subgroup of $F$ of all elements fixed by $\beta$ is (topologically) infinitely generated; however this is not always the case if $p$ divides the order of $\beta$.

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