Groupes quotient: Quotients de groupe

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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.