Group Actions: Examples and Applications

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Related lectures (32)

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Group Actions: Theory and Examples

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

Group Theory Basics: Subgroups and Homomorphisms

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

Group Theory Basics

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

Subsets and subgroups associated with an action

Explores subsets and subgroups related to group actions on sets.

Active Learning: Group Homomorphisms

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

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.

Subsets and subgroups associated with an action

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

Push-out and Quotients

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

Class Equation and Burnside's Lemma

Explores the class equation and Burnside's lemma in group theory.