Lectures related to Finitely generated abelian group

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

Explores the classification of finite abelian groups and rings, emphasizing elementary divisors and properties of rings.

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.

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

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

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

Focuses on abelian p-groups, demonstrating technical results for classifying finite abelian groups.

Presents the classification of finite abelian groups as products of cyclic groups, a fundamental result in various branches of mathematics.

Covers the properties of linear molecules in carbon and discusses neutral elements, associative law, and conjugate elements.

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

Explores exact sequences of abelian group homomorphisms and provides examples.

Covers useful lemmas for p-groups, including divisibility properties and the existence of specific elements in finite abelian groups.

Explores conjugation in groups, the direct product of groups, and the classification of finite abelian groups.

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

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

Explores the study of finite groups through subgroup analysis, focusing on Sylow subgroups.

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

Explores Hermite-Minkowski theorems in number fields and ideal classes.