Lectures related to Class Equation and Burnside's Lemma

Basic Notions, Ch III: Group Actions

Explores group actions on sets, orbits, fixed points, and classic results.

Important Facts of Fixed Points and Orbits

Explores group actions, fixed points, orbits, Equation of Class, and Burnside's Lemma.

Group Actions: Examples and Applications

Explores examples of group actions on sets, emphasizing the utility of group actions to understand groups.

Class Equation and Burnside's Lemma

Covers the class equation in group theory and Burnside's Lemma, relating orbits and fixed points.

Classification of Extensions

Explores the classification of extensions in group theory, emphasizing split extensions and semi-direct products.

Group Theory Fundamentals

Introduces group theory basics and group action concepts with associated subsets.

Points fixes et orbites

Covers fixed points, orbits, and stabilizer subgroups in group actions.

Active Learning: Group Homomorphisms

Explores group homomorphisms, emphasizing surjective mappings and their impact on group questions.

Fixed Points and Orbits Analysis: Group Actions

Explores the definition of orbits and fixed points of a G-object in any category, focusing on G-equivariant applications.

Subsets and subgroups associated with an action

Explores subsets, subgroups, actions, fixed points, stabilizers, orbits, and bijections in group theory.

Subsets and subgroups associated with an action

Explores subsets and subgroups related to group actions on sets.

Two Definitions of Group Action

Explores two definitions of group action on a set, focusing on properties and applications.

Group Actions: Theory and Examples

Explores concrete examples of group actions on sets, focusing on actions that do not change the set.

Recap of Group Theory

Provides a recap of group theory, defining a group as a set with a multiplication operation.

Group Theory Basics: Subgroups and Homomorphisms

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

Useful Variants on Beta Action

Covers abelian groups, Sylow subgroups, and variants on beta action.

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.

Group Theory: Special Cases

Covers special cases in group theory, focusing on group actions and functors.

Group Theory: Actions and Stabilizers

Explores group actions, subsets, points fixes, orbits, and stabilizers.

Amalgams: Group Pushouts

Covers the concept of amalgams, defining pushouts and quotient groups in group theory.