Direct Sum of Subgroups

Related lectures (30)

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

Covers direct sums of abelian groups, group actions, and vector spaces, including coproducts and homomorphisms.

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

Explores the concept of direct sums in abelian groups, emphasizing the universal property and homomorphisms.

Introduces Lemma 1.14 for finite sets in Ab and discusses notations and properties of direct sums.

Explores the construction and properties of the free abelian group FAb(X) and its categorical extensions.

Covers group actions, conjugacy classes, centralizers, direct products, and finite abelian groups.

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.