Lecture

Conjugation in Groups

Related lectures (30)

Covers group actions, conjugacy classes, centralizers, direct products, and finite abelian groups.

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

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

Covers Cauchy's theorem, classification of finite abelian groups, direct product properties, and more.

Covers the proof of the Classification Theorem for finite abelian groups, demonstrating the existence of a decomposition into cyclic groups.

Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.

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.

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

Explores the arithmetic of direct sums in group theory, discussing conditions for equality.

Explores the concept of direct sums in abelian groups, emphasizing the universal property and homomorphisms.

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

Covers the classification theorem for finite abelian groups and introduces rings, including zero divisors and domains.

Explores k-fold degenerate sets of eigenfunctions and their basis for irreducible representations.

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

Explores direct sums in group theory, focusing on abelian groups and their implications.

Delves into direct sums of abelian groups, showcasing their coproduct properties and universal verification.

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

Covers the existence and uniqueness of direct sums in abelian groups.