Lectures related to Sylow Subgroups: Group Theory

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

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

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

Focuses on demonstrating properties using Lemma 3.4 in group theory.

Explores the Hom functor in Abelian groups, focusing on its construction and properties.

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

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

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

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