Group Actions: Examples and Applications

This lecture explores various examples of group actions on sets, including actions on subsets and subgroups. The instructor discusses the utility of group actions to better understand groups themselves, focusing on stabilizers, orbits, and fixed points. The lecture also covers actions by translation and conjugation, with a generalization to homomorphisms. Additionally, the concept of actions of a group on its subgroups is introduced, highlighting the importance of understanding how groups can act on their subgroups.