Homomorphisms and Isomorphisms

This lecture covers the concepts of homomorphisms and isomorphisms in group theory, focusing on defining them and exploring their properties. It discusses the conditions for a function to be a homomorphism and the sufficiency of being injective. The lecture also delves into the notion of isomorphism, emphasizing the importance of bijectivity. Additionally, it touches on the completion of group tables, the center of a group, and the relationship between kernels and images. The instructor demonstrates the application of these concepts through examples and exercises, highlighting the significance of universal product ownership and the Chinese Remainder Theorem.