The Theory of Groups

by Hall, Marshall

• ISBN13: 9780486816906
• ISBN10: 0486816907
• Edition: Reprint
• Format: Paperback
• Copyright: 2018-02-15
• Publisher: Dover Publications

Summary

"Mastering the contents of Hall's book will lead a student to the frontiers of group theory. He will be well equipped to read any recent literature and start original research himself in this field ... This remarkable book undoubtedly will become a standard text on group theory." — Eugene Guth, American Scientist
"This is a book which I wish I could put in the hands of every graduate student who has shown an interest in the elements of group theory. The first 10 chapters would give him an excellent foundation in group theory, and there would still remain 10 chapters for his delight." — Richard Hubert Bruck, American Mathematical Monthly
This encyclopedic treatment of the current knowledge of group theory was widely praised upon its 1959 publication for its readability and accessibility. Today this volume remains useful as an unsurpassed resource for learning and reviewing the basics of a fundamental and ever-expanding area of modern mathematics. Suitable for advanced undergraduate mathematics majors and graduate students in math, the treatment is largely self-contained and offers numerous helpful exercises.

Author Biography

Marshal Hall, Jr., (1910–1990) worked in Naval Intelligence during World War II, including six months in 1944 at Bletchley Park in the UK, the famed center of British codebreaking. He taught at Ohio State from 1946 until 1959, when he joined the faculty at the California Institute of Technology. In 1971 he became the first IBM Professor at Caltech, the first named chair in math. He retired from Caltech in 1981 and later taught at Emory University. In addition to group theory, he made significant contributions to combinatorics and other areas.

Table of Contents

1. INTRODUCTION

2. NORMAL SUBGROUPS AND HOMOMORPHISMS

3. ELEMENTARY THEORY OF ABELIAN GROUPS

4. SYLOW THEOREMS

5. PERMUTATION GROUPS

6. AUTOMORPHISMS

7. FREE GROUPS

8. LATTICES AND COMPOSITION SERIES

9. A THEOREM OF FROBENIUS; SOLVABLE GROUPS

10. SUPERSOLVABLE AND NILPOTENT GROUPS

11. BASIC COMMUTATORS

12. THE THEORY OF p-GROUPS; REGULAR p-GROUPS

13. FURTHER THEORY OF ABELIAN GROUPS

14. MONOMIAL REPRESENTATIONS AND THE TRANSFER

15. GROUP EXTENSIONS AND COHOMOLOGY OF GROUPS

16. GROUP REPRESENTATION

17. FREE AND AMALGAMATED PRODUCTS

18. THE BURNSIDE PROBLEM

19. LATTICES OF SUBGROUPS

20. GROUP THEORY AND PROJECTIVE PLANES

BIBLIOGRAPHY

INDEX

INDEX OF SPECIAL SYMBOLS