Abelian Groups deals with the theory of abelian or commutative groups, with special emphasis on results concerning structure problems. More than 500 exercises of varying degrees of difficulty, with and without hints, are included. Some of the exercises illuminate the theorems cited in the text by providing alternative developments, proofs or counterexamples of generalizations. Comprised of 16 chapters, this volume begins with an overview of the basic facts on group theory such as factor group or homomorphism. The discussion then turns to direct sums of cyclic groups, divisible groups, and direct summands and pure subgroups, as well as Kulikov's basic subgroups. Subsequent chapters focus on the structure theory of the three main classes of abelian groups: the primary groups, the torsion-free groups, and the mixed groups. Applications of the theory are also considered, along with other topics such as homomorphism groups and endomorphism rings; the Schreier extension theory with a discussion of the group of extensions and the structure of the tensor product. In addition, the book examines the theory of the additive group of rings and the multiplicative group of fields, along with Baer's theory of the lattice of subgroups. This book is intended for young research workers and students who intend to familiarize themselves with abelian groups.

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Yes, you can access Abelian Groups by L. Fuchs, J. P. Kahane,A. P. Robertson,S. Ulam in PDF and/or ePUB format, as well as other popular books in Mathematics & Algebra. We have over one million books available in our catalogue for you to explore.

Information

Publisher

Pergamon

Year

2014

ISBN

9781483280905

Edition

Topic

Mathematics

Subtopic

Algebra

Index

Mathematics

Front Cover
Abelian Groups
Copyright Page
Table of Contents
PREFACE
TABLE OF NOTATIONS
CHAPTER I. BASIC CONCEPTS. THE MOST IMPORTANT GROUPS
CHAPTER II. DIRECT SUM OF CYCLIC GROUPS
CHAPTER III. DIVISIBLE GROUPS
CHAPTER IV. DIRECT SUMMANDS AND PURE SUBGROUPS
CHAPTER V. BASIC SUBGROUPS
CHAPTER VI. THE STRUCTURE OF p-GROUPS
CHAPTER VII. TORSION FREE GROUPS
CHAPTER VIII. MIXED GROUPS
CHAPTER IX. HOMOMORPHISM GROUPS AND ENDOMORPHISM RINGS
CHAPTER X. GROUP EXTENSIONS
CHAPTER XI. TENSOR PRODUCTS
CHAPTER XII. THE ADDITIVE GROUP OF RINGS
CHAPTER XIII. THE MULTIPLICATIVE GROUP OF FIELDS
CHAPTER XIV. THE LATTICE OF SUBGROUPS
CHAPTER XV. DECOMPOSITIONS INTO DIRECT SUMS OF SUBSETS
CHAPTER XVI. VARIOUS QUESTIONS
BIBLIOGRAPHY
AUTHOR INDEX
SUBJECT INDEX
ERRATA