Lectures related to Sylow Subgroups: Group Theory

Sylow Subgroups: Structure and Properties

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

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Existence of Sylow Subgroups: Proof by Recurrence

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

Hom Functor: Abelian Groups

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

A Tool for Demonstrating Properties: Lemme 3.4

Focuses on demonstrating properties using Lemma 3.4 in group theory.

Functor Hom: Abelian Groups

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

Free Abelian Groups: Group Theory

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

Symmetry and Group Theory

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

Finitely Generated Abelian Groups

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

Resoluble Groups: Quotients of Group

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

Divisibility and Torsion

Explores divisibility and torsion in group theory, focusing on defining a functor that preserves divisibility.

Introduction to Group Theory

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

Group Theory: Active Learning Session

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

Torsion: Hom Functoriality and Exact Sequences

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

Useful Variants on Beta Action

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

Group Actions: Equivariance and Functors

Explores equivariance in group actions and functors, demonstrating its importance in group theory.

Simplicial and Cosimplicial Objects: Examples and Applications

Covers simplicial and cosimplicial objects in category theory with practical examples.

Introduction, Ch V: Sylow Subgroups

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

Abelian Groups: First Approach

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

Groups: Definitions, Properties, and Homomorphisms

Introduces the basic concepts of groups, including definitions, properties, and homomorphisms, with a focus on subgroup properties and normal subgroups.