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The Theory of Groups: Second Edition
Marshall Hall, Jr.

AMS Chelsea Publishing
1959; 434 pp; hardcover
Volume: 288
ISBN-10: 0-8218-1967-4
ISBN-13: 978-0-8218-1967-8
List Price: US$55
Member Price: US$49.50
Order Code: CHEL/288.H
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See also:

Finite Group Theory - I Martin Isaacs

Perhaps the first truly famous book devoted primarily to finite groups was Burnside's book. From the time of its second edition in 1911 until the appearance of Hall's book, there were few books of similar stature. Hall's book is still considered to be a classic source for fundamental results on the representation theory for finite groups, the Burnside problem, extensions and cohomology of groups, \(p\)-groups and much more. For the student who has already had an introduction to group theory, there is much treasure to be found in Hall's Theory of Groups.

From the Preface: "The present volume is intended to serve a dual purpose. The first ten chapters are meant to be the basis for a course in group theory, and exercises have been included at the end of each of these chapters. The last ten chapters are meant to be useful as optional material in a course or as reference material. When used as a text, the book is intended for students who have had an introductory course in modern algebra comparable to a course taught from Birkhoff and Mac Lane's A Survey of Modern Algebra. I have tried to make this book as self-contained as possible, but where background material is needed references have been given, chiefly to Birkhoff and Mac Lane."


Graduate students and research mathematicians.


"... still a very good introduction to the subject."

-- Zentralblatt MATH

"By some inexplicable trick of memory, the reviewer, in reading this book, recaptured all the excitement of his first reading of Burnside ... He recommends the volume with enthusiasm."

-- Mathematical Reviews

Table of Contents

  • Introduction
  • Normal subgroups and homomorphisms
  • Elementary theory of abelian groups
  • Sylow theorems
  • Permutation groups
  • Automorphisms
  • Free groups
  • Lattices and composition series
  • A theorem of Frobenius; solvable groups
  • Supersolvable and nilpotent groups
  • Basic commutators
  • The theory of \(p\)-groups; regular \(p\)-groups
  • Further theory of abelian groups
  • Monomial representations and the transfer
  • Group extensions and cohomology of groups
  • Group representation
  • Free and amalgamated products
  • The Burnside problem
  • Lattices of subgroups
  • Group theory and projective planes
  • Bibliography
  • Index
  • Index of special symbols
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