  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.
