Finite Abelian Groups: Classification Theorem

This lecture reaches the climax of the chapter by presenting the classification of finite abelian groups. This fundamental result describes any finite abelian group as a product of cyclic groups of prime power order, extensively used in algebra, algebraic topology, algebraic geometry, number theory, etc. The proof, not too difficult with the tools learned in previous lessons, involves demonstrating the existence and uniqueness of certain sequences of positive integers, along with technical lemmas and arguments by induction.