Groups & Rings: Morphisms, Kernels, and Injectivity

Related lectures (31)

Page 3 of 4

Explores the universal property of groups, defining homomorphisms and exploring subgroup properties.

Covers normal subgroups, quotient groups, homomorphisms, and the categorical viewpoint in group theory.

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

Explores group homomorphisms, constructing isomorphisms between groups using generators and relations.

Covers Lagrange's theorem, group homomorphisms, congruence classes, and normal subgroups.

Explores the isomorphism theorems for quotient groups and the concept of surjective homomorphisms.

Covers the concept of morphism of groups, actions on sets, and automorphisms.

Delves into the second isomorphism theorem in group theory, emphasizing subgroup relationships and quotient groups.

Explores a categorical perspective on group quotients, focusing on a specific case.

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