Lectures related to Applications of Lagrange's Theorem

Applications of Lagrange's Theorem

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

Lagrange's Theorem: Applications and Homomorphisms

Covers Lagrange's theorem, group homomorphisms, congruence classes, and normal subgroups.

Group Theory: Quotients of Group

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

Group Theory Basics: Subgroups and Homomorphisms

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

Normal Subgroups and Quotients

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

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.

Subgroups and Cosets: Lagrange's Theorem

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

Push-out and Quotients

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

Groups & Rings: Morphisms, Kernels, and Injectivity

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

Group Theory Basics

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

Pushouts in Group Theory: Universal Properties Explained

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

Topology: Free Groups and Their Properties

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

Group Homomorphisms: Kernels, Images, and Normal Subgroups

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

Group Actions: Examples and Applications

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

Symmetric Group: Cycle Notation

Explores the symmetric group, emphasizing cycle notation and group properties.

RSA Cryptosystem: Encryption and Decryption Process

Covers the RSA cryptosystem, encryption, decryption, group theory, Lagrange's theorem, and practical applications in secure communication.

Active Learning: Group Homomorphisms

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

Automorphism Groups: Trees and Graphs III

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

Isomorphism Theorems: Third Isomorphism Theorem

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