Groups & Rings: Morphisms, Kernels, and Injectivity

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Related lectures (31)

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Push-out and Quotients

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

Group Homomorphisms: Kernels, Images, and Normal Subgroups

Explores group homomorphisms, kernels, images, and normal subgroups, using the dihedral group D_n as an example.

First Isomorphism Theorem

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

Pushouts in Group Theory: Universal Properties Explained

Covers the construction and universal properties of pushouts in group theory.

Fundamental Groups

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

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.

Homomorphisms and Isomorphisms

Explores homomorphisms, isomorphisms, group properties, and their applications through examples and exercises.

Classification of Extensions

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

Applications of Lagrange's Theorem

Explores the applications of Lagrange's theorem in algebra, covering corollaries, cyclic groups, and quotient groups.

Abelian Groups: Free Abelian Groups

Explores free abelian groups, homomorphisms, and exact sequences in group theory.