Lectures related to Finite Cas X and Notations

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

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

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

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

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

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

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

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

Explores the direct sum of subgroups in an abelian group and introduces the coproduct concept in Abelian categories.