Groups & Subgroups: Definitions, Theorems, and Morphisms

Related lectures (28)

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Explores the group structure and isomorphism of elliptic curves, including inverses, associativity, and compactification to the torus.

Discusses linear Lie groups, their definitions, properties, and the relationship between integral curves and vector fields.

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

Explores fundamental properties of groups and numbers, emphasizing equivalence classes and subgroup concepts.

Explores symmetries in physics through group theory, emphasizing how symmetries keep equations of motion unchanged.

Explores the action of Hamiltonian homeomorphisms on surfaces and discusses related mathematical concepts.

Covers the basics of categories and functors, exploring properties, composition, and uniqueness in category theory.

Introduces group theory concepts, including definitions and properties of groups, rings, and fields.

Covers the basics of group theory, including sets, applications, and examples like permutations and rotations.

Explores permutations preserving adjacency, linear transformations, groups, and sub-groups.