Lectures related to Groupes quotient: Quotients de groupe

Amalgams: Group Pushouts

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

Chinese Remainder Theorem: Rings and Fields

Covers the Chinese remainder theorem for commutative rings and integers, polynomial rings, and Euclidean domains.

Group Theory: Quotients of Group

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

Principal Ideal Domains: Structure and Homomorphisms

Covers the concepts of ideals, principal ideal domains, and ring homomorphisms.

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.

Quotients de groupe: Un cas particulier

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

Isomorphism Theorems: Third Isomorphism Theorem

Explores the third isomorphism theorem in group theory, focusing on quotient groups and a categorical perspective.

Abelianization of Fundamental Group

Explores abelianization examples, homomorphisms, and isomorphisms in group theory.

Quotient Groups: Homomorphisms and Isomorphisms

Explores quotient groups, homomorphisms, isomorphisms, and push-outs in different categories.

Group Cohomology

Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.

Quotient Groups and Homomorphisms

Covers explicit calculations of push-outs in Ens and the study of induced homomorphisms between quotient groups.

Push-out and Quotients

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

First Isomorphism Theorem

Covers the first isomorphism theorem in group theory and its applications.

Symmetric Group: Cycle Notation

Explores the symmetric group, emphasizing cycle notation and group properties.

Ring Homomorphisms and Ideals

Explores ring homomorphisms, bilateral ideals, ring features, and ideal operations.

Isomorphism Theorems: Quotients of Group

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

Group Actions: Theory and Examples

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

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.

Applications of Lagrange's Theorem

Explores Lagrange's theorem applications in group theory and arithmetic, focusing on subgroups, cosets, quotient groups, and homomorphisms.

Homomorphisms: Birational Maps and Affine Varieties

Covers homomorphisms between affine varieties, birational maps, regular groups, and connectedness.