Abstract
Let G be an infinite finitely generated pro-p group acting on a pro-p tree such that the restriction of the action to some open subgroup is free. We prove that G splits over an edge stabilizer either as an amalgamated free pro-p product or as a pro-p \({\text {HNN}}\)-extension. Using this result, we prove under a certain condition that free pro-p products with procyclic amalgamation inherit from its amalgamated free factors the property of each 2-generated pro-p subgroup being free pro-p. This generalizes known pro-p results, as well as some pro-p analogues of classical results in abstract combinatorial group theory.
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Pavel Zalesskii and Theo Zapata are grateful for the partial financial support from CNPq and CAPES.
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Dedicated to Jean-Pierre Serre for his ninetieth birthday.
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Herfort, W., Zalesskii, P. & Zapata, T. Splitting theorems for pro-p groups acting on pro-p trees. Sel. Math. New Ser. 22, 1245–1268 (2016). https://doi.org/10.1007/s00029-015-0217-7
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DOI: https://doi.org/10.1007/s00029-015-0217-7