Lectures related to Symmetry and Group Theory

Subgroups and Cosets: Lagrange's Theorem

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

Untitled

Applications of Lagrange's Theorem

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

Group Homomorphisms

Explores group homomorphisms, constructing isomorphisms between groups using generators and relations.

Finitely Generated Abelian Groups

Explores finitely generated abelian groups, focusing on their structure and isomorphism theorems.

Fundamental Groups

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

Group Theory: Reducible and Irreducible Representations

Explores group theory in quantum physics, emphasizing reducible and irreducible representations, conservation laws, and group properties.

Representation Theory: Algebras and Homomorphisms

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Untitled

Local structure of totally disconnected locally compact groups III

Explores the local structure of totally disconnected locally compact groups and their isomorphisms through conjugation.

Abelian Groups: First Approach

Introduces the theory of abelian groups, focusing on p-abelian groups and their structure.

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.

Ideals and Representations

Covers ideals, representations, modules, and maximal ideals in associative algebras.

Symmetry and Group Theory: Exercise Set 4

Explores symmetry operations, isomorphic representations, and three-dimensional group representations.

Dihedral Group: Symmetries and Cosets

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

Direct Sums Arithmetic

Explores the arithmetic of direct sums in group theory, discussing conditions for equality.

Torsion and Divisibility: Abelian Groups

Introduces torsion and divisibility concepts in abelian groups to describe their structure.

Existence of Sylow Subgroups: Proof by Recurrence

Demonstrates the existence of p-Sylow subgroups in any finite group using induction and the abelian case.

Bases of Representations: Summary and Rules

Covers the summary and rules related to bases of representations in Symmetry 2021.

Linear Molecules: Carbon

Covers the properties of linear molecules in carbon and discusses neutral elements, associative law, and conjugate elements.