Subsets and subgroups associated with an action

This lecture covers the concept of subsets and subgroups associated with a group action on a set, defining actions, fixed points, stabilizers, orbits, and bijections between quotient groups. The instructor explains the notation and definitions step by step, providing propositions and proofs to illustrate the concepts. The lecture emphasizes the relationship between group elements and their actions on sets, highlighting the importance of understanding the stabilizers and orbits in group theory.