Lectures related to Introduction to Group Theory

Covers abelian groups, Sylow subgroups, and variants on beta action.

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

Delves into group theory, emphasizing the centralizer of elements and the classification of finite abelian groups.

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

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

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

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

Covers the verification of constructions in the context of abelian groups and Sylow subgroups.

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

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

Delves into direct sums of abelian groups, showcasing their coproduct properties and universal verification.

Focuses on demonstrating properties using Lemma 3.4 in group theory.

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

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

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

Introduces torsion and divisibility concepts in abelian groups to describe their structure.

Explores group operations with cyclic properties and the universal ownership of quotients.

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

Explores the arithmetic of direct sums in group theory, discussing conditions for equality.