The Theory of Groups (AMS Chelsea Publishing) - Hardcover

Hall, Marshall, Jr.

Hardcover

ISBN 10: 0821819674 ISBN 13: 9780821819678

Publisher: American Mathematical Society, 1999

Synopsis

This volume is intended to serve a dual purpose. The first ten chapters form the basis for a course in Group Theory, including exercises at the end of each chapter. The final ten chapters are designed as useful optional material in a course or as reference material. When used as a textbook, this book is intended for students who have had an introductory course in Modern Algebra (such as that taught from Birkhoff and MacLane's A Survey of Modern Algebra). This book was developed from lecture notes on a course of Group Theory delivered by the author at Ohio State University over a period of years, The first ten chapters (the core course) covers: 1. Algebraic Laws, Definitions for Groups; Subgroups, Cosets, etc. 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 The final ten chapters of reference material covers: 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 Hardback in burgundy cloth, ppxiii, 434, including Bibliography, Index, and Index of Special Symbols.

About this title

Synopsis:

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 Bumside 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 to the second edition (1976): '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'.

About the Author:

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.

About this edition

• Publisher: American Mathematical Society
• Publication date: 1999
• ISBN 10: 0821819674
• ISBN 13: 9780821819678
• Binding: Hardcover