Existence: Proof of Classification Theorem

This lecture covers the proof of the Classification Theorem for finite abelian groups, demonstrating that any finite abelian group is isomorphic to a direct sum of cyclic groups. The instructor explains the process of proving this theorem by induction on the order of the group, showing that each cyclic group is a p-group. The lecture also discusses the existence of a decomposition into cyclic groups for any abelian p-group. The presentation concludes with the affirmation that any abelian group can be represented as a direct sum of cyclic groups, providing a detailed explanation of the proof.