Lectures related to Group Theory: Active Learning Session

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

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

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

Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.

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

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

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

Covers ideals, representations, modules, and maximal ideals in associative algebras.

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Explores Lie Algebra's connection to Group Theory through associative operations and Jacobi identities.

Covers examples of group algebra decomposition and simple infinite-dimensional algebras.

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

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

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

Covers active learning, video lectures, exercises, categories, group actions, and abelian groups.

Explores Lie groups, scalar fields, and vector spaces transformations.

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

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

Explores chain complexes, abelian groups, homomorphisms, homology groups, and free abelian groups.