Lectures related to Group Fundamental: Structure and Applications

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Explores Cayley tables, group operations, homomorphisms, Lie groups, and differentiable groups.

Covers the construction and universal properties of pushouts in group theory.

Covers concrete categories with sets and structures, including Ens, Gr, Ab, and Vectk.

Explores group homomorphisms, Euler's phi function, and group products.

Covers the concept of amalgams, defining pushouts and quotient groups in group theory.

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

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

Explores group homomorphisms, isomorphisms, and generators in abstract algebra.