Group Quotients and Push-outs

This lecture covers the concept of group quotients and push-outs, exploring when a group is isomorphic to a quotient of another group. It delves into the demonstration of isomorphisms and provides examples to illustrate the concepts. The lecture also discusses the existence of isomorphisms and push-outs in different scenarios, highlighting the importance of surjectivity in determining isomorphism. Additionally, it explains the notion of push-outs in category theory and how they can be defined explicitly. The instructor presents various cases and examples to help understand the topic thoroughly.