A Course in Group Theory

Paperback | April 30, 1999

byJohn F. Humphreys

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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 fundamentalclassification theorems in finite group theory, and the text is further explained in numerous examples and exercises, and summaries at the end of each chapter.

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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 fundamentalclassification theorems in finite group theo...

John Humphreys is at University of Liverpool.

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Format:PaperbackDimensions:304 pages, 9.21 × 6.14 × 0.67 inPublished:April 30, 1999Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198534590

ISBN - 13:9780198534594

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Table of Contents

1. Definitions and examples2. Maps and relations on sets3. Elementary consequences of the definitions4. Subgroups5. Cosets and Lagrange's Theorem6. Error-correcting codes7. Normal subgroups and quotient groups8. The Homomorphism Theorem9. Permutations10. The Orbit-Stabilizer Theorem11. The Sylow Theorems12. Applications of Sylow Theorems13. Direct products14. The classification of finite abelian groups15. The Jordan-Holder Theorem16. Composition factors and chief factors17. Soluble groups18. Examples of soluble groups19. Semi-direct products and wreath products20. Extensions21. Central and cyclic extensions22. Groups with at most 31 elements23. The projective special linear groups24. The Mathieu groups25. The classification of finite simple groupsAppendix A Prerequisites from Number Theory and Linear AlgebraAppendix B Groups of order 32Appendix C Solutions to ExercisesBibliographyIndex

Editorial Reviews

`Clear and fast moving, as you'd expect from this author.'New Scientist, Ian Stewart, September 1996,