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arXiv · 1103.2955

Splitting theorems for pro-$p$ groups acting on pro-$p$ trees and 2-generated subgroups of free pro-$p$ products with procyclic amalgamations

Wolfgang Herfort·Pavel Zalesskii·Theo Zapata
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Abstract

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.

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Wolfgang Herfort, Pavel Zalesskii, Theo Zapata. 2013-06-17. Splitting theorems for pro-$p$ groups acting on pro-$p$ trees and 2-generated subgroups of free pro-$p$ products with procyclic amalgamations. https://arxiv.org/abs/1103.2955

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