Lectures related to Universal Property of G*H

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

Covers the Zig Zag Lemma and the long exact sequence of relative homology.

Covers induced homomorphisms on relative homology groups and their properties.

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

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

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

Explores the third isomorphism theorem in group theory, focusing on quotient groups and a categorical perspective.

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

Covers the concept of the free product in group theory and how to determine monomorphisms and homomorphisms.