Lectures related to Lattice of subgroups

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.

Local structure of totally disconnected locally compact groups I

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

Covers self-similar groups and automorphisms of rooted trees, exploring residually finite groups and congruence subgroups.

Groupes résolubles: Quotients and Subgroups

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

McKay Correspondence and Coxeter Groups

Explores the McKay correspondence, Coxeter groups, and finite subgroups of SU(2) and SO(3, emphasizing odd order properties and root system constructions.

Solvable Groups: Part 1

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

Groups and Products

Covers the concepts of groups, products, and homomorphisms, focusing on the hx set and group alternates.

Subgroups and subalgebras

Explores the unique determination of homomorphisms by differentials and the intersection of closed subgroups' Lie algebras.

Group Homomorphisms: Kernels, Images, and Normal Subgroups

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

Vector Valued Functions

Explores vector valued functions, their representations, uniqueness, and congruence subgroups.

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.

Fundamental Groups

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

Subgroups Criteria: Propositions and Examples

Covers the criteria for subgroups and provides examples and proofs.

Subgroups and Generators

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

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: Subgroups and General Group Actions

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

Group Theory Basics: Subgroups and Homomorphisms

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

Group Theory: Introduction

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