Lecture
This lecture covers the concept of quotient groups, where a group is decomposed into disjoint left classes of a subgroup, each having the same cardinality. It explains the application that maps elements of the group to their left classes, leading to a group structure for G/N. The lecture also discusses the characterization of equality of left classes, independent of the normality of N, and the unique homomorphism from G/N to H when N is a subgroup of ker. The presentation concludes with a categorical perspective after reviewing fundamental concepts from the first year.