Automorphism Groups: Essential Chief Series

This lecture covers the concept of essential chief series in tdlc groups, focusing on the work by Reid-Wesolek. It explains the construction of closed, normal subgroups in tdlc groups and their chief factors. The lecture also discusses the uniqueness statements related to compactly generated tdlc groups. The connection with the modular function is explored, emphasizing the rational values of the function. Various propositions and theorems are presented to illustrate the theoretical framework behind automorphism groups of trees and graphs. The lecture concludes with applications of the established concepts to Cayley-Abels graphs and the proof of essential chief series.