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Premium Chapters
Preface
1/19/2025
About This Book
1/19/2025
Introduction to Group Theory
1/19/2025
Definitions and Examples
1/19/2025
Basic Properties of Groups
1/19/2025
Finite and Infinite Groups
1/19/2025
Symmetry and Permutation Groups
1/19/2025
Matrix Groups
1/19/2025
Dihedral Groups
1/19/2025
Historical Background
1/19/2025
Subgroups and Cyclic Groups
1/19/2025
Subgroup Criteria
1/19/2025
Examples of Subgroups
1/19/2025
Cyclic Groups and Generators
1/19/2025
Properties of Cyclic Groups
1/19/2025
Order of an Element
1/19/2025
Subgroups of Cyclic Groups
1/19/2025
Applications of Cyclic Groups
1/19/2025
Group Homomorphisms and Isomorphisms
1/19/2025
Kernel and Image
1/19/2025
Properties of Homomorphisms
1/19/2025
The Isomorphism Theorems
1/19/2025
Automorphisms
1/19/2025
Endomorphisms
1/19/2025
Applications of Homomorphisms
1/19/2025
Cosets and Lagrange’s Theorem
1/19/2025
Cosets and Their Properties
1/19/2025
Lagrange’s Theorem
1/19/2025
Applications of Lagrange’s Theorem
1/19/2025
Index of a Subgroup
1/19/2025
Normalizers and Centralizers
1/19/2025
The Counting Principle
1/19/2025
Applications in Symmetry
1/19/2025
Normal Subgroups and Quotient Groups
1/19/2025
Normal Subgroups: Definition and Examples
1/19/2025
Properties of Normal Subgroups
1/19/2025
Quotient Groups
1/19/2025
The First Isomorphism Theorem
1/19/2025
The Second and Third Isomorphism Theorems
1/19/2025
The Correspondence Theorem
1/19/2025
Applications of Quotient Groups
1/19/2025
Group Actions and Sylow Theorems
1/19/2025
Group Actions: Definition and Examples
1/19/2025
Transitive Group Actions
1/19/2025
The Orbit-Stabilizer Theorem
1/19/2025
Applications of Group Actions
1/19/2025
Sylow Theorems: Introduction
1/19/2025
Proofs of Sylow Theorems
1/19/2025
Applications of Sylow Theorems
1/19/2025
Advanced Topics in Group Theory
1/19/2025
Solvable and Nilpotent Groups
1/19/2025
Free Groups
1/19/2025
Group Presentations
1/19/2025
Commutator Subgroups
1/19/2025
Group Extensions
1/19/2025
Simple Groups
1/19/2025
Recent Developments in Group Theory
1/19/2025