Lectures related to Group Theory: Isomorphism and Semi-Direct Product

Discusses linear Lie groups, their definitions, properties, and the relationship between integral curves and vector fields.

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

Presents the Lemma of the Five, a fundamental result in group theory.

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

Delves into the second isomorphism theorem in group theory, emphasizing subgroup relationships and quotient groups.

Covers the theory of groups and homotopical algebra, emphasizing natural transformations, identities, and isomorphism of categories.

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

Covers the application and proof of the Lagrange theorem in group theory.

Explores group quotients and push-outs, discussing isomorphisms and surjectivity in different scenarios.