Lectures related to Morphism of Groups

Introduces subgroups and homomorphisms in group theory, with examples for illustration.

Covers the first isomorphism theorem in group theory and its applications.

Explores group morphisms, injectivity criteria, and conjugation concepts within groups.

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

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

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

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

Explores the classification of extensions in group theory, emphasizing split extensions and semi-direct products.

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