Lectures related to Group Theory: Introduction

Group Theory Basics: Subgroups and Homomorphisms

Introduces subgroups and homomorphisms in group theory, with examples for illustration.

Group Theory Fundamentals

Introduces group theory basics and group action concepts with associated subsets.

Group Actions: Examples and Applications

Explores examples of group actions on sets, emphasizing the utility of group actions to understand groups.

Group Theory: Subgroups and General Group Actions

Explores group actions, defining functors on groups, and verifying properties of group actions.

Subgroups and Cosets: Lagrange's Theorem

Explores subgroups, normal subgroups, cosets, and Lagrange's theorem in group theory, emphasizing the importance of left cosets.

Powers and Multiples: Subgroups and Stabilizers

Covers powers, multiples, subgroups, and stabilizers in group theory.

Symmetry and Group Theory

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

Group Theory Basics

Introduces the basics of group theory, covering definitions, examples, subgroups, and homomorphisms.

Subsets and subgroups associated with an action

Explores subsets, subgroups, actions, fixed points, stabilizers, orbits, and bijections in group theory.

Subsets and subgroups associated with an action

Explores subsets and subgroups related to group actions on sets.

Subgroups and Generators

Covers subgroups, generators, cyclic groups, and group morphisms in group theory.

Group Theory: Reducible and Irreducible Representations

Explores group theory in quantum physics, emphasizing reducible and irreducible representations, conservation laws, and group properties.

Categorical Perspective: Group Quotients

Explores the categorical sense of constructing a group quotient by a normal subgroup, showing it as a specific example of a more general construction.

Groups: Definitions, Properties, and Homomorphisms

Introduces the basic concepts of groups, including definitions, properties, and homomorphisms, with a focus on subgroup properties and normal subgroups.

Local structure of totally disconnected locally compact groups I

Covers the local structure of totally disconnected locally compact groups, exploring properties and applications.

Direct Sums Arithmetic

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

Combinatorial Group Theory

Introduces combinatorial group theory, emphasizing group presentations, normal subgroups, and group quotients.

Group Presentations

Covers the concept of group presentations using generators and relations to define groups.

Second Isomorphism Theorem

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

Push-out and Quotients

Delves into push-out and quotients in group theory, emphasizing homomorphisms and normal subgroups.