Group Theory: Verification

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Related lectures (31)

Page 3 of 4

Amalgams: Group Pushouts

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

Topology: Free Groups and Their Properties

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

Algebra: Chain Complexes

Explores chain complexes, abelian groups, homomorphisms, homology groups, and free abelian groups.

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.

Groups and Homomorphisms

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

Existence of Sylow Subgroups: Proof by Recurrence

Demonstrates the existence of p-Sylow subgroups in any finite group using induction and the abelian case.

Fundamental Groups

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

Group Operations and Quotients

Explores group operations with cyclic properties and the universal ownership of quotients.

Resoluble Groups: Quotients of Group

Covers the definition of solvable groups and the abelian property of group quotients.

Classification of Extensions

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