Group Actions: Theory and Examples

This lecture explores concrete examples of group actions on sets. The instructor discusses the basic definitions and properties of group actions, focusing on actions that do not change the set. Various examples of group actions are presented, illustrating how groups can act on themselves and on other sets. The lecture also covers the concept of homomorphisms and how they can be used to define group actions. The discussion extends to actions by translation and conjugation, highlighting the significance of these actions in group theory.