Homomorphisms and Isomorphisms

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Related lectures (32)

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First Isomorphism Theorem

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

Fundamental Groups

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

Uniqueness of Amalgams

Explores the uniqueness of amalgams in group theory through examples and diagrams.

Groups & Rings: Morphisms, Kernels, and Injectivity

Explores group morphisms, kernels, and injectivity in group theory.

Universal Property of Groups

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

Applications of Lagrange's Theorem

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

Groups and Homomorphisms

Covers Euler's totient function, group theory, homomorphisms, and group isomorphisms.

Group Cohomology

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

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.

Schur's Lemma and Representations

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