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.
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 < 32 ; Appendix C Solutions to Exercises ; Bibliography ; Index
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