Lectures related to Group Theory Fundamentals

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.

Group Theory Basics: Subgroups and Homomorphisms

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

Fundamental Groups

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

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.

Group Theory Basics

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

Isomorphism Theorems: Third Isomorphism Theorem

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

Group Actions: Examples and Applications

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

Push-out and Quotients

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

Universal Property of Groups

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

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Group Theory: Quotients of Group

Covers normal subgroups, quotient groups, homomorphisms, and the categorical viewpoint in group theory.

Class Equation and Burnside's Lemma

Covers the class equation in group theory and Burnside's Lemma, relating orbits and fixed points.

Active Learning: Group Homomorphisms

Explores group homomorphisms, emphasizing surjective mappings and their impact on group questions.

Normal Subgroups and Quotients

Introduces normal subgroups, group quotients, and their applications in group theory.

Class Equation and Burnside's Lemma

Explores the class equation and Burnside's lemma in group theory.

Groups & Rings: Morphisms, Kernels, and Injectivity

Explores group morphisms, kernels, and injectivity in group theory.

Group Theory: Introduction

Covers group theory fundamentals, motivations for studying group actions, equivalent definitions, and subsets associated with group actions.

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Pushouts in Group Theory: Universal Properties Explained

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

Automorphism Groups: Trees and Graphs III

Explores automorphism groups of trees and graphs, including actions on trees and group homomorphisms.