# Book:Joseph A. Gallian/Contemporary Abstract Algebra/Seventh Edition

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## Joseph A. Gallian:

## Joseph A. Gallian: *Contemporary Abstract Algebra (7th Edition)*

Published $2009$, **Brooks Cole**

- ISBN 0-547-16509-9.

## Subject Matter

## Contents

- Preface

**Part 1: Integers and Equivalence Relations**- Chapter 0: Preliminaries

**Part 2: Groups**- Chapter 1: Introduction to Groups
- Chapter 2: Groups
- Chapter 3: Finite Groups, Subgroups
- Chapter 4: Cyclic Groups
- Chapter 5: Permutation Groups
- Chapter 6: Isomorphisms
- Chapter 7: Cosets and Lagrange's Theorem
- Chapter 8: External Direct Products
- Chapter 9: Normal Subgroups and Factor Groups
- Chapter 10: Group Homomorphisms
- Chapter 11: Fundamental Theorem of Finite Abelian Groups

**Part 3: Rings**- Chapter 12: Introduction to Rings
- Chapter 13: Integral Domains
- Chapter 14: Ideals and Factor Rings
- Chapter 15: Ring Homomorphisms
- Chapter 16: Polynomial Rings
- Chapter 17: Factorization of Polynomials
- Chapter 18: Divisibility in Integral Domains

**Part 4: Fields**- Chapter 19: Vector Spaces
- Chapter 20: Extension Fields
- Chapter 21: Algebraic Extensions
- Chapter 22: Finite Fields
- Chapter 23: Geometric Constructions

**Part 5: Special Topics**- Chapter 24: Sylow Theorems
- Chapter 25: Finite Simple Groups
- Chapter 26: Generators and Relations
- Chapter 27: Symmetry Groups
- Chapter 28: Frieze Groups and Crystallographic Groups
- Chapter 29: Symmetry and Counting
- Chapter 30: Cayley Digraphs of Groups
- Chapter 31: Introduction to Algebraic Coding Theory
- Chapter 32: An Introduction to Galois Theory
- Chapter 33: Cyclotomic Extensions

- Selected Answers

- Text Credits

- Photo Credits

- Index of Mathmaticians

- Index of Terms