Contents
Chapter 1: Integers and Permutations
1.2 Divisors and Prime Factorization
2.4 Cyclic Groups and the Order of an Element
2.5 Homomorphisms and Isomorphisms
2.6 Cosets and Lagrange's Theorem
2.7 Groups of Motions and Symmetries
2.11 An Application to Binary Linear Codes
3.1 Examples and Basic Properties
3.2 Integral Domains and Fields
4.2 Factorization of Polynomials over a Field
4.3 Factor Rings of Polynomials over a Field
Chapter 5: Factorization in Integral Domains
5.1 Irreducibles and Unique Factorization
6.7 An Application to Cyclic and BCH Codes
Chapter 7: Modules over Principal Ideal Domains
7.2 Modules over a Principal Ideal Domain
Chapter 8: p-Groups and the Sylow Theorems
8.6 An Application to Combinatorics
Chapter 9: Series of Subgroups
10.1 Galois Groups and Separability
10.2 The Main Theorem of Galois Theory
10.3 Insolvability of Polynomials
10.4 Cyclotomic Polynomials and Wedderburn's Theorem
Chapter 11: Finiteness Conditions for Rings and Modules