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

2011/03/15 by Herfort, Wolfgang, Zalesskii, Pavel, Zapata, Theo · 1 citation
#20E06 #20E18 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1103.2955

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.

Cited by

• Residual profiles and bounded generation in pro-p completions of amalgamated products

Related

• Virtually free pro-p products
• Pro-p groups acting on trees with finitely many maximal vertex stabilizers up to conjugation
• Generalized Stallings' decomposition theorem for pro-p groups
• Cyclic splittings of pro-C groups
• Kurosh Subgroup Theorem in Free Pro-p Products