Quotient Groups and Homomorphisms

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Related lectures (32)

Page 3 of 4

Covers the group presentation of S3, normal subgroups, generators, relations, quotient groups, and injective homomorphisms.

Homomorphisms: Birational Maps and Affine Varieties

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

Fundamental Groups

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

Applications of Lagrange's Theorem

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

Quotient Groups: Homomorphisms and Isomorphisms

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

Amalgams: Group Pushouts

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

Quotients in Abelian Groups

Covers quotients in abelian groups and the concept of free abelian groups, showing that every abelian group is isomorphic to a quotient of a free abelian group.

Isomorphism Theorems: Third Isomorphism Theorem

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

Topology: Free Groups and Their Properties

Discusses the theory of free groups, their properties, and relationships with other algebraic structures.

Group Cohomology

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