The structure of some virtually free pro-$p$ groups
Claus Scheiderer
Fakult\"at f\"ur Mathematik, Universit\"at Regensburg, 93040 Regensburg, 
Germany 
Proc. Amer. Math. Soc. 127 (1999), 695-700.

Abstract. We prove two conjectures on pro-$p$ groups made by Herfort, Ribes 
and Zalesskii. The first says that a finitely generated pro-$p$ group which 
has an open free pro-$p$ subgroup of index $p$ is a
free pro-$p$ product $H_0 * (S_1 \times H_1) * \cdots * (S_m \times H_m)$, 
where the $H_i$ are free pro-$p$ of finite rank and the $S_i$ are cyclic of 
order $p$. The second says that if $F$ is a free pro-$p$ group
of finite rank and $S$ is a finite $p$-group of automorphisms of $F$, then 
$\text{\rm Fix}(S)$ is a free factor of $F$. The proofs use cohomology, and 
in particular a ``Brown theorem'' for profinite groups.