Groups of automorphisms of rooted trees have been studied for years as an important source of groups with interesting properties. For instance, the Grigorchuk group (that is a group acting on the binary tree) is the first example of a finitely generated group with intermediate growth (this answered an open question posed by Milnor) and the first example of an amenable but not elementary amenable group. Furthermore, this group provides a counterexample to the General Burnside Problem.
In these lectures we will first introduce the basic theory of groups of automorphisms of rooted trees and their subgroups. Then we will give examples and main properties of such groups, including the aforementioned Grigorchuk group, and the GGS groups.
This video is part of the London Mathematical Society‘s Online Graduate Lecture Series. These are supported by the LMS, and organized by the North British Geometric Group Theory Seminar.
