An introduction to group theory

This book was written in the summer of 1992 in the Radar Division of the NRL and is in the public domain. It is document PU/NRL/5350-92-231. Typed into latex by David Joyner ([email protected]).

• Contents
• Preliminaries
  • Sets and mappings
    • Exercises
  • Number theory
    • Exercises
  
  
• Introduction to Groups
  • Definition of a group
  • Some consequences of the axioms
    • Elementary Properties of Groups
  • Exercises for Chapter 2
  
  
• Permutations
  • Cycles and cycle notation
    • Exercises
  • Transpositions
    • Exercises
  
  
• Subsets of a Group and Lagrange's Theorem
  • Conjugacy
    • Exercises
  • Subsets of a group
    • Exercises
  • Cosets and Lagrange's Theorem
    • Exercises
  
  
• Generating Sets, Cyclic Groups and Isomorphisms
  • Generators and isomophisms
    • Exercises
  • Cyclic Groups
    • Exercises
  
  
• Factor Groups
  • Normal subgroups
    • Exercises
  • Factor groups
    • Exercises
  • Simple groups
    • Exercises
  
  
• Homomorphisms
  • Definition and Elementary Properties
    • Exercises
  • Special Homomorphisms and Isomorphisms
    • Exercises
  
  
• Solvable Groups, Double Cosets and Isomorphism Theorems
  • Commutators and solvable groups
    • Exercises
  • Double cosets
    • Exercises
  • Isomorphism theorems
    • Exercises
  
  
• Direct Products
  • External and internal direct product
    • Exercises
  • Applications and further properties
    • Exercises
  
  
• The Sylow Theorems
  • Existence of Sylow subgroups; the first Sylow Theorem
    • Exercises
  • The second and third Sylow Theorems
    • Exercises
  • Applications
    • Exercises
  
  
• Solvable Groups and the Jordan-Hölder Theorem
  • The third isomorphism theorem
    • Exercises
  • Series of groups; solvable groups revisited
    • Exercises
  • The Jordan-Hölder Theorem
    • Exercises
  
  
• Bibliography
• Index
• About this document ...