Finite Abelian Groups & Rings

Related lectures (30)

Page 3 of 3

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

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

Introduces the theory of abelian groups, focusing on p-abelian groups and their structure.

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

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

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

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

Explores invariant definitions in sets, groups, and automorphisms, including p-divisible groups and free abelian groups.

Covers the local structure of totally disconnected locally compact groups, exploring properties and applications.

Covers technical lemmas on abelian p-groups and maximal order elements.