AMS Chelsea Publishing 1959; 434 pp; hardcover Volume: 288 ISBN10: 0821819674 ISBN13: 9780821819678 List Price: US$55 Member Price: US$49.50 Order Code: CHEL/288.H
 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 selfcontained as possible, but where background material is needed references have been given, chiefly to Birkhoff and Mac Lane." Readership Graduate students and research mathematicians. Reviews "... 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
