Simple groups of automorphisms of trees determined by their actions on finite subtrees

2013/12/09 by Banks, Christopher C., Elder, Murray, Willis, George A.
#20E08 #20E32 #22D05 #22F50 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1312.2311

Abstract

We introduce the notion of the k-closure of a group of automorphisms of a locally finite tree, and give several examples of the construction. We show that the k-closure satisfies a new property of automorphism groups of trees that generalises Tits' Property P. We prove that, apart from some degenerate cases, any non-discrete group acting on a tree with this property contains an abstractly simple subgroup.

Related

• Automorphism Groups of Trees: Generalities and Prescribed Local Actions
• Finitely Presented Groups Acting on Trees
• An introduction to the local-to-global behaviour of groups acting on trees and the theory of local action diagrams
• Groups Acting on Trees With Prescribed Local Action
• Groups acting on trees with Tits' independence property (P)