Next:
Contents
Contents
Index
An introduction to group theory
Tony Gaglione
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 ...
David Joyner
2001-04-12
