Groups and Homomorphisms

Related lectures (31)

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Explores the Hom functor for abelian groups and its relation to direct sums.

Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.

Explores the universal property of groups, defining homomorphisms and exploring subgroup properties.

Explores the uniqueness of amalgams in group theory through examples and diagrams.

Explores chirality, group completeness, Abelian groups, conjugate classes, and isomorphic groups in symmetry and group theory.

Explores direct sums in group theory, focusing on abelian groups and their implications.

Explores group homomorphisms, constructing isomorphisms between groups using generators and relations.

Explores the Hom functor in Abelian groups, focusing on its construction and properties.

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