%0 Journal Article
%T Splitting theorems for pro-$p$ groups acting on pro-$p$ trees and 2-generated subgroups of free pro-$p$ products with procyclic amalgamations
%A Wolfgang Herfort
%A Pavel Zalesskii
%A Theo Zapata
%J Mathematics
%D 2011
%I arXiv
%X Let G be a finitely generated infinite pro-p group acting on a pro-p tree such that the restriction of the action to some open subgroup is free. Then we prove that G splits as a pro-p amalgamated product or as a pro-p HNN-extension over an edge stabilizer. Using this result we prove under certain conditions that free pro-p products with procyclic amalgamation inherit from its free factors the property of each 2-generated subgroup being free pro-p. This generalizes known pro-p results, as well as some pro-p analogs of classical results in abstract combinatorial group theory.
%U http://arxiv.org/abs/1103.2955v2