Generic groups acting on regular trees

2007/02/25 by Abert, Miklos, Glasner, Yair
#05C25 #20B15 #20D35 #20E08 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.math/0702736

Abstract

Let T be a k-regular tree (k>2) and A its automorphism group. We analyze a generic finitely generated subgroup Gamma of A. We show that Gamma is free and establish a trichotomy on the closure of Gamma: it is either discrete, compact or has index at most 2 in A.

Related

• Simple groups of automorphisms of trees determined by their actions on finite subtrees
• Most actions on regular trees are almost free
• Automorphism Groups of Trees: Generalities and Prescribed Local Actions
• Rooted trees, strong cofinality and ample generics
• Normal subgroups of groups acting on trees and automorphism groups of\n graphs