Group homomorphism

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Related lectures (31)

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Groupes quotient: Quotients de groupe

Explores quotient groups, left classes decomposition, group structure, and unique homomorphisms.

Concrete Categories

Covers concrete categories with sets and structures, including Ens, Gr, Ab, and Vectk.

Schur's Lemma and Representations

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.

Recap of Group Theory

Provides a recap of group theory, defining a group as a set with a multiplication operation.

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.

Push-out: Categorical Perspective on Quotients

Explores the concept of push-out in group homomorphisms.

First Isomorphism Theorem

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

Chinese Remainder Theorem: Rings and Fields

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

Push-out and Quotients

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

Group Theory Basics: Subgroups and Homomorphisms

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