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Concept

Subgroup

Related lectures (32)

Subsets and subgroups associated with an action

Explores subsets and subgroups related to group actions on sets.

Automorphism Groups: Trees and Graphs III

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

Diffie-Hellman Key Exchange

Explores the Diffie-Hellman key exchange protocol, covering computational challenges, subgroup issues, and key wrapping in RFC 2631.

Local structure of totally disconnected locally compact groups I

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

Group Theory Basics: Subgroups and Homomorphisms

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

Solvable Groups: Part 1

Covers the concept of solvable groups and their decomposition into abelian pieces, exploring various properties and examples.

Definition: Understanding Group Structures

Explores the philosophy of understanding a group through its subgroups' structure, focusing on finite groups.

Groupes résolubles: Quotients and Subgroups

Explores the concept of solvable groups and their subgroups' impact on solvability.

Symmetry and Group Theory

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

Cohomology Groups: Hopf Formula

Explores the Hopf formula in cohomology groups, emphasizing the 4-term exact sequence and its implications.

Untitled

Group Theory: Introduction

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

Symmetries in Physics

Explores symmetries in physics through group theory, emphasizing how symmetries keep equations of motion unchanged.

Second Isomorphism Theorem

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

Mathematical Parenthesis on Groups and Lagrange Theorem Log in to Mediaspace to watch this video

Explores cosets in commutative groups, Lagrange theorem, and integer factorization.

Subgroups and Cosets: Lagrange's Theorem Log in to Mediaspace to watch this video

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

Lagrange's Theorem: Applications and Homomorphisms Log in to Mediaspace to watch this video

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

Universal Property of Groups Log in to Mediaspace to watch this video

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

Dihedral Group: Symmetries and Cosets Log in to Mediaspace to watch this video

Explores the symmetries of a regular n-gon, normal subgroups, cosets, and Lagrange's theorem.

Categorical Perspective: Group Quotients Log in to Mediaspace to watch this video

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