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Integers and Equivalence Relations
0 Preliminaries 1
Introduction to Groups 7
Groups
2 Groups 9
3 Finite Groups; Subgroups 13
1 4 Cyclic Groups 20
5 Permutation Groups 27
6 Isomorphisms 34
7 Cosets and Lagrange’s Theorem 40
8 External Direct Products 46
9 Normal Subgroups and Factor Groups 53
10 Group Homomorphisms 59
11 Fundamental Theorem of Finite Abelian Groups 65
12 Introduction to Rings 69
13 Integral Domains 74
14 Ideals and Factor Rings 80
15 Ring Homomorphisms 87
16 Polynomial Rings 94
17 Factorization of Polynomials 100
18 Divisibility in Integral Domains 105
Special Topics
24 Sylow Theorems 129
25 Finite Simple Groups 135
26 Generators and Relations 140
27 Symmetry Groups 144
28 Frieze Groups and Crystallographic Groups 146
29 Symmetry and Counting 148
30 Cayley Digraphs of Groups 151
31 Introduction to Algebraic Coding Theory 154
32 An Introduction to Galois Theory 158
33 Cyclotomic Extensions 161
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