Abelian p-groups: Groupes abéliens

Related lectures (30)

Page 3 of 3

Explores the existence of p-Sylow subgroups in finite groups and the abelian group center.

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

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

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

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

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

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

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

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

Explores the concept of torsion in group theory, focusing on its Hom functoriality and its role in exact sequences.