Normal subgroups of groups acting on trees and automorphism groups of\n graphs

2012/09/17 by Rögnvaldur G. Möller, Möller, Rögnvaldur G., Jan Vonk +1
Computer Science · #05C25 #20B27 #20E08 #Advanced Graph Theory Research #FOS: Mathematics #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1209.3625

openalex publication_date 2012/09/17 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

Let T be a tree and e an edge in T. If C is a component of\nT\∖ e and both C and its complement are infinite we say that C is\na half-tree. The main result of this paper is that if G is a closed subgroup\nof the automorphism group of T and G leaves no non-trivial subtree\ninvariant and fixes no end of T then the subgroup generated by the pointwise\nstabilizers of half-trees is topologically simple. This result is used to\nderive analogues of recent results of Caprace and De Medts (2011) and it is\nalso applied in the study of the full automorphism group of a locally finite\nprimitive graph with infinitely many ends.\n

Related

• Simple groups of automorphisms of trees determined by their actions on finite subtrees
• Automorphism Groups of Trees: Generalities and Prescribed Local Actions
• Amenability of groups acting on trees
• Generic groups acting on regular trees
• Boundedly simple groups of automorphisms of trees