紹介
This book is an excellent and self-contained introduction to the theory of groups, covering all topics likely to be encountered in undergraduate courses. It aims to stimulate and encourage undergraduates to find out more about their subject. The book takes as its theme the various fundamental classification theorems in finite group theory, and the text is further explained in numerous examples and exercises, and summaries at the end of each chapter. This book is intended for first, second and third year undergraduates and first year postgraduates studying group theory.
目次
1. Definitions and examples
2. Maps and relations on sets
3. Elementary consequences of the definitions
4. Subgroups
5. Cosets and Lagrange's Theorem
6. Error-correcting codes
7. Normal subgroups and quotient groups
8. The Homomorphism Theorem
9. Permutations
10. The Orbit-Stabilizer Theorem
11. The Sylow Theorems
12. Applications of Sylow Theorems
13. Direct products
14. The classification of finite abelian groups
15. The Jordan-Holder Theorem
16. Composition factors and chief factors
17. Soluble groups
18. Examples of soluble groups
19. Semi-direct products and wreath products
20. Extensions
21. Central and cyclic extensions
22. Groups with at most 31 elements
23. The projective special linear groups
24. The Mathieu groups
25. The classification of finite simple groups
Appendix A Prerequisites from Number Theory and Linear Algebra
Appendix B Groups of order less than 32
Appendix C Solutions to Exercises
Bibliography
Index
