Algebra: Group Actions and Direct Products

Related lectures (30)

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Covers the Orbit-Stabilizer theorem, conjugacy classes, and direct products in finite groups.

Explores conjugation in groups, the direct product of groups, and the classification of finite abelian groups.

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.

Explores abelian groups from a categorical perspective, discussing the coproduct construction.

Demonstrates the existence of direct sums of abelian groups and covers propositions and proofs related to their uniqueness.

Covers the classification of finite abelian groups and the unique sequence of positive integers for isomorphism.

Explores the Hom functor for abelian groups and its relation to direct sums.

Explores the concept of free abelian groups as an important left adjoint functor.

Explores the classification of finite abelian groups and rings, emphasizing elementary divisors and properties of rings.