Lectures related to Existence of Direct Sums: Abelian Groups

Covers the existence and uniqueness of direct sums in abelian groups.

Explores finitely generated abelian groups, focusing on their structure and isomorphism theorems.

Explores direct sums in abelian groups, emphasizing existence and uniqueness.

Explores the direct sum of abelian groups, emphasizing bijections and uniqueness.

Covers the proof of the Classification Theorem for finite abelian groups, demonstrating the existence of a decomposition into cyclic groups.

Covers the Orbit-Stabilizer theorem, conjugacy classes, and direct products in finite groups.

Explores the isomorphism between Hom(A, B) and Hom(A, B) for any abelian group B.

Covers the definition of solvable groups and the abelian property of group quotients.

Explores the concept of torsion in group theory, focusing on its Hom functoriality and its role in exact sequences.