Active Learning: Group Homomorphisms

This lecture covers the concept of group homomorphisms, focusing on surjective homomorphisms and their implications on group questions. The instructor explains the importance of subjectivity in homomorphisms, the properties of surjective homomorphisms, and the relationship between normal subgroups and group actions. The lecture also delves into the definition and properties of actions of a group on the set of its subgroups, including the concept of stabilizers and normalizers. The discussion extends to actions without fixed points and examples illustrating different types of group actions. The lecture concludes with a reflection on the existence of actions without fixed points in general group settings.