The Theory of Groups

"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.

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.

1. INTRODUCTION2. NORMAL SUBGROUPS AND HOMOMORPHISMS3. ELEMENTARY THEORY OF ABELIAN GROUPS4. SYLOW THEOREMS5. PERMUTATION GROUPS6. AUTOMORPHISMS7. FREE GROUPS8. LATTICES AND COMPOSITION SERIES9. A THEOREM OF FROBENIUS; SOLVABLE GROUPS10. SUPERSOLVABLE AND NILPOTENT GROUPS11. BASIC COMMUTATORS12. THE THEORY OF p-GROUPS; REGULAR p-GROUPS13. FURTHER THEORY OF ABELIAN GROUPS14. MONOMIAL REPRESENTATIONS AND THE TRANSFER15. GROUP EXTENSIONS AND COHOMOLOGY OF GROUPS16. GROUP REPRESENTATION17. FREE AND AMALGAMATED PRODUCTS18. THE BURNSIDE PROBLEM19. LATTICES OF SUBGROUPS20. GROUP THEORY AND PROJECTIVE PLANESBIBLIOGRAPHYINDEXINDEX OF SPECIAL SYMBOLS