Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.
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.