A course in group theory

John F. Humphreys

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.

「Nielsen BookData」より


  • 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

「Nielsen BookData」より


書名 A course in group theory
著作者等 Humphreys, John Francis
Humphreys J. F.
出版元 Oxford Univ. Press
刊行年月 1996
ページ数 xii, 279 p.
大きさ 24 cm
ISBN 0198534531
NCID BA27762332
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言語 英語
出版国 イギリス