Mathematics – Group Theory


Mathematics - Group Theory

Mathematics – Group Theory:

The Theory of Groups

Marshall Hall, Jr.

This mathematics textbook 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) cover:

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 cover:

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.

VG (ex-library, with usual lib paraphernalia on prelims.; contents tight and clean); no dustjacket.

Chelsea Publishing Company, New York, 1976. Second Edition

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