Group Actions: Theory and Examples

Related lectures (31)

Page 3 of 4

Explores two definitions of group action and their equivalence through bijection in group homomorphisms.

Covers the generalities of functions, including the definition of an application between sets and the uniqueness of elements in the image set.

Explores edge labels, skills like aggregation and deduction, and the structure of contents.

Covers simplicial and cosimplicial objects in category theory with practical examples.

Discusses the theory of free groups, their properties, and relationships with other algebraic structures.

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

Introduces Cartesian product and induction for proofs using integers and sets.

Covers aggregation queries and sorting of results in Geographic Information Systems.

Explores the motivations for studying actions through the universal action of bijections.

Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.