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

Finitely Generated Abelian Groups

Explores finitely generated abelian groups, focusing on their structure and isomorphism theorems.

Fundamental Groups

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

Isomorphism: Order of Group Elements

Explores isomorphism and the order of group elements, emphasizing matching identities and inverses.

Local structure of totally disconnected locally compact groups III

Explores the local structure of totally disconnected locally compact groups and their isomorphisms through conjugation.

Symmetry and Group Theory

Explores chirality, group completeness, Abelian groups, conjugate classes, and isomorphic groups in symmetry and group theory.

Algebraic Structures: Small Order Groups

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

Commutative Groups: Foundations for Cryptography

Covers commutative groups and their significance in cryptography.

Group Homomorphisms

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

Uniqueness of Amalgams

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

Isomorphism in Aut(p)

Explores isomorphism between Aut(p) and a Galois covering through topology course notes.

Pushouts in Group Theory: Universal Properties Explained

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

Isomorphism Theorems: Third Isomorphism Theorem

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

Introduction to Group Theory: Motivation

Introduces adjunctions in Group Theory with examples of natural transformations and isomorphisms.

Schur's Lemma and Representations

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

Exact Sequences: Splitting Remarks

Explores split exact sequences in group theory with a focus on characterization and isomorphisms.

Morphism of Groups

Covers the concept of morphism of groups, actions on sets, and automorphisms.

Subrepresentations of the regular representation

Explores subrepresentations of the regular representation in group theory, emphasizing properties and isomorphism between subrepresentations.

Group Theory: Part 2

Delves into advanced group theory concepts such as isomorphisms and homomorphisms.

Applications of Lagrange's Theorem

Explores the applications of Lagrange's theorem in algebra, covering corollaries, cyclic groups, and quotient groups.

Topology: Fundamental Groups and Applications

Provides an overview of fundamental groups in topology and their applications, focusing on the Seifert-van Kampen theorem and its implications for computing fundamental groups.