Concept

Abelian group

Related lectures (31)

Explores character representations in group repetition theory, discussing irreducibility, equivalence, and associated values.

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

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

Explores the arithmetic of direct sum of abelian groups and the process of turning a monoid into a commutative group.

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

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

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

Explores the properties and structure of Sylow subgroups in group theory, emphasizing a theorem-independent approach.

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

Covers the properties of linear molecules in carbon and discusses neutral elements, associative law, and conjugate elements.

Covers the properties of commutative linear algebraic groups and their elements.

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

Explores chirality, group completeness, Abelian groups, conjugate classes, and isomorphic groups in symmetry and group theory.

Covers exact sequences, torsion, divisibility, and operations on abelian groups.

Covers commutative groups and their significance in cryptography.

Explores exact sequences of abelian group homomorphisms and provides examples.

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

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

Covers a review of algebraic structures such as rings, fields, and groups, including integral domains, ideals, and finite fields.

Explores the concept of p-subgroups of Sylow in group theory, emphasizing the philosophy of studying mathematical objects 'one prime at a time'.