Symmetry and Group Theory

About
Privacy
Disclaimer

Graph Chatbot

Related lectures (30)

Page 2 of 3

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.