Applications of Lagrange's Theorem

This lecture covers the application of Lagrange's theorem in group theory and arithmetic, focusing on the group of units in Z_n, Euler's theorem, Fermat's little theorem, normal subgroups, quotient groups, and group homomorphisms. It explains how Lagrange's theorem relates to the order of elements in a group, the index of subgroups, and the properties of cosets. The lecture also delves into the concept of quotient groups, emphasizing the formation of a group from cosets of a normal subgroup. Additionally, it explores the significance of the image and kernel of a group homomorphism.