Direct sum of groups

Related lectures (31)

Covers the concept of the sum of vector subspaces in an IR-vector space.

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

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

Covers the concept of eigenfunctions of H as bases for irreducible representations and integrals.

Covers Cauchy's theorem, classification of finite abelian groups, direct product properties, and more.

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

Covers the Jordan normal form and the decomposition of vector spaces by an endomorphism.

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

Explores the Lie theorem and irreducible representations in group theory.

Explores the arithmetic of direct sum of abelian groups and the process of turning a monoid into a commutative group.

Explores direct products in group theory, including semi-direct products and group properties.

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