Lagrange's Theorem: Applications and Homomorphisms

This lecture covers Lagrange's theorem and its applications, such as the index of a subgroup in a finite group. It also discusses group homomorphisms, including examples and properties of homomorphisms of additive groups. The lecture introduces congruence classes modulo n and the concept of normal subgroups. Additionally, it explores the relationship between cosets and normal subgroups, as well as the properties of neutral elements in groups. The instructor demonstrates how to determine if a subgroup is normal in a group and explains the significance of invertible elements forming a group. The lecture concludes with examples of homomorphisms and subgroup properties in groups.