Lectures related to Groups & Rings: Morphisms, Kernels, and Injectivity

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

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: Subgroups and Homomorphisms

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

Automorphism Groups: Trees and Graphs III

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

Group Theory Basics

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

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Applications of Lagrange's Theorem

Explores Lagrange's theorem applications in group theory and arithmetic, focusing on subgroups, cosets, quotient groups, and homomorphisms.

Topology: Free Groups and Their Properties

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

Group Actions: Examples and Applications

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

Active Learning: Group Homomorphisms

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

Push-out and Quotients

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

Group Homomorphisms: Kernels, Images, and Normal Subgroups

Explores group homomorphisms, kernels, images, and normal subgroups, using the dihedral group D_n as an example.

First Isomorphism Theorem

Covers the first isomorphism theorem in group theory and its applications.

Pushouts in Group Theory: Universal Properties Explained

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

Fundamental Groups

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

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.

Homomorphisms and Isomorphisms

Explores homomorphisms, isomorphisms, group properties, and their applications through examples and exercises.

Classification of Extensions

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

Applications of Lagrange's Theorem

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

Abelian Groups: Free Abelian Groups

Explores free abelian groups, homomorphisms, and exact sequences in group theory.