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Book Categories |
Preface | ||
Ch. I | Preliminaries - Groups and Rings | 1 |
1 | Introduction to Groups | 2 |
2 | Quotient Groups and Sylow Subgroups | 16 |
3 | Finite Abelian Groups and Solvable Groups | 34 |
4 | Introduction to Rings | 43 |
5 | Factoring in F[x] | 60 |
Ch. II | Field Extensions | 72 |
1 | Simple Extensions | 72 |
2 | Algebraic Extensions | 88 |
3 | Splitting Fields and Normal Extensions | 97 |
Ch. III | The Galois Correspondence | 110 |
1 | The Fundamental Correspondence | 110 |
2 | The Solvable Correspondence | 150 |
Ch. IV | Applications | 163 |
1 | Constructibility | 163 |
2 | Roots of Unity | 173 |
3 | Wedderburn's Theorem | 181 |
4 | Dirichlet's Theorem and Finite Abelian Groups | 183 |
App. A | Groups | 188 |
App. B | Factoring in Integral Domains | 211 |
App. C | Vector Spaces | 230 |
Bibliography | 237 | |
Index | 239 |
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