Lectures related to Group Quotients: Push-out Uniqueness

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

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

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

Delves into direct sums of abelian groups, showcasing their coproduct properties and universal verification.

Explores k-fold degenerate sets of eigenfunctions and their basis for irreducible representations.

Covers the basis for irreducible representations and characters of direct product representations.

Explores direct products in group theory, including semi-direct products and group properties.

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

Discusses the theory of free groups, their properties, and relationships with other algebraic structures.

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

Explores small order groups, group morphisms, and the second isomorphism theorem.

Explores abelian groups from a categorical perspective, discussing the coproduct construction.

Explores active learning in Group Theory, focusing on products, coproducts, adjunctions, and natural transformations.

Explores Coxeter groups, emphasizing generators, relations, and unique presentations in group theory.

Demonstrates the existence of direct sums of abelian groups and covers propositions and proofs related to their uniqueness.

Covers group actions, conjugacy classes, centralizers, direct products, and finite abelian groups.

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

Covers group theory concepts like isomorphism and semi-direct product through examples and proofs.

Explores the arithmetic of direct sums in group theory, discussing conditions for equality.

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