Class Equation and Burnside's Lemma

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Group Theory Basics

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

Orbit of a G-ensemble

Explores orbits in a G-ensemble, functions of fixed points, and G-equivariance.

Fundamental Groups

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

Push-out and Quotients

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

Categorical Perspective: Abelian Groups

Explores abelian groups from a categorical perspective, discussing the coproduct construction.

Homomorphism of Groups: Signature

Explores homomorphisms of groups, focusing on the signature sgn and the concept of cycles and transpositions.

Functor Fixed Points and Orbital Functor

Explores defining functors on morphisms, fixed points, orbits, equivariance, and composition preservation.

Uniqueness of Amalgams

Explores the uniqueness of amalgams in group theory through examples and diagrams.

Active Learning: Group Theory

Explores adjoint functors, points fixes, orbits, and non-trivial actions 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.