Groups & Subgroups: Definitions, Theorems, and Morphisms

Related lectures (31)

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

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

Covers subgroups, generators, cyclic groups, and group morphisms in group theory.

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

Covers examples of categories like sets, groups, and vector spaces, exploring composition and product formation.

Explores group actions, defining functors on groups, and verifying properties of group actions.

Explores finitely generated abelian groups, focusing on their structure and isomorphism theorems.

Explains linear independence, bases, and dimension in vector spaces, including the importance of the order of vectors in a basis.

Explores martingales, Brownian movement, mean numbers, and generation hypotheses.

Explores the derivation of Dynkin diagrams from Du Val singularities.

Covers rings and modules, emphasizing color codes and homological algebra concepts.

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