Categorical Perspective: Abelian Groups

Related lectures (31)

Page 3 of 4

Introduces Lemma 1.14 for finite sets in Ab and discusses notations and properties of direct sums.

Explores the applications of Lagrange's theorem in algebra, covering corollaries, cyclic groups, and quotient groups.

Explores Cayley tables, group operations, homomorphisms, Lie groups, and differentiable groups.

Explores direct products in group theory, including semi-direct products and group properties.

Explores isometries, group homomorphisms, linear transformations, and group generation by similarities.

Explores free abelian groups, homomorphisms, exact sequences, and functors in group theory.

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

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

Explores exact sequences of abelian group homomorphisms and provides examples.

Covers Euler's totient function, group theory, homomorphisms, and group isomorphisms.