Group Homomorphisms

This lecture covers the concept of group homomorphisms, defining maps between groups that preserve the group structure. It explains the properties of homomorphisms, such as the preservation of the group operation and the neutral element. The lecture also introduces the notion of group isomorphisms, which are bijective homomorphisms indicating that two groups are essentially the same. Examples and exercises are provided to illustrate these concepts, including the construction of group isomorphisms. Additionally, the lecture discusses generators of a group, which are elements that can generate the entire group through their products and inverses.