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

Autor:	Herfort, Wolfgang, Zalesskii, Pavel, Zapata, Theo
Rok vydání:	2011
Předmět:	Mathematics - Group Theory 20E18 20E06
Druh dokumentu:	Working Paper
Popis:	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. Comment: 21 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1103.2955 Zobrazit plný text záznamu View this record from Arxiv