Automorphism groups of trees and graphs II

This lecture delves into the uniqueness of trees and the automorphism groups of trees and graphs, focusing on the local action and prune content. The instructor discusses Cayley-Abels graphs, vertex stabilizers, and constructing vertex-transitive subgroups with prescribed local actions. The lecture also covers the compactness of automorphism groups, point stabilizers, and the local prime content of tdlc groups. Various theorems and exercises are presented, including the relationship between dihedral groups and Cayley-Abels graphs. The content concludes with insights into legal colorings of trees and the Burger-Mozes universal group.