Group Theory: Quotients of Group

This lecture reviews the concepts of normal subgroups and the group formed by the set of left cosets of a normal subgroup, known as the quotient group. It also covers the universal property of the construction of the quotient group, emphasizing the importance of normality in the process. The lecture delves into the properties of homomorphisms, injectivity conditions, and the group structure of g/n. The instructor illustrates the decomposition of a group into disjoint left cosets and the homomorphism mapping elements to their respective cosets. The lecture concludes with a categorical perspective on the topic.