Cover for Abelian Groups

Abelian Groups

Book • Third Edition1960

Author:

L. FUCHS

Abelian Groups

Book • Third Edition1960

 

Cover for Abelian Groups

Author:

L. FUCHS

About the book

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Book description

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 ... read full description

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  2. Book chapterAbstract only

    CHAPTER I - BASIC CONCEPTS. THE MOST IMPORTANT GROUPS

    Pages 13-36

  3. Book chapterAbstract only

    CHAPTER II - DIRECT SUM OF CYCLIC GROUPS

    Pages 37-56

  4. Book chapterAbstract only

    CHAPTER III - DIVISIBLE GROUPS

    Pages 57-70

  5. Book chapterAbstract only

    CHAPTER IV - DIRECT SUMMANDS AND PURE SUBGROUPS

    Pages 71-96

  6. Book chapterAbstract only

    CHAPTER V - BASIC SUBGROUPS

    Pages 97-110

  7. Book chapterAbstract only

    CHAPTER VI - THE STRUCTURE OF p-GROUPS

    Pages 111-144

  8. Book chapterAbstract only

    CHAPTER VII - TORSION FREE GROUPS

    Pages 145-184

  9. Book chapterAbstract only

    CHAPTER VIII - MIXED GROUPS

    Pages 185-204

  10. Book chapterAbstract only

    CHAPTER IX - HOMOMORPHISM GROUPS AND ENDOMORPHISM RINGS

    Pages 205-232

  11. Book chapterAbstract only

    CHAPTER X - GROUP EXTENSIONS

    Pages 233-248

  12. Book chapterAbstract only

    CHAPTER XI - TENSOR PRODUCTS

    Pages 249-257

  13. Book chapterAbstract only

    CHAPTER XII - THE ADDITIVE GROUP OF RINGS

    Pages 258-294

  14. Book chapterAbstract only

    CHAPTER XIII - THE MULTIPLICATIVE GROUP OF FIELDS

    Pages 295-299

  15. Book chapterAbstract only

    CHAPTER XIV - THE LATTICE OF SUBGROUPS

    Pages 300-314

  16. Book chapterAbstract only

    CHAPTER XV - DECOMPOSITIONS INTO DIRECT SUMS OF SUBSETS

    Pages 315-331

  17. Book chapterAbstract only

    CHAPTER XVI - VARIOUS QUESTIONS

    Pages 332-352

  18. Book chapterNo access

    BIBLIOGRAPHY

    Pages 353-361

  19. Book chapterNo access

    AUTHOR INDEX

    Pages 363-364

  20. Book chapterNo access

    SUBJECT INDEX

    Pages 365-367

  21. Book chapterNo access

    ERRATA

    Page ibc1

About the book

Description

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.

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.

Details

ISBN

978-0-08-009206-5

Language

English

Published

1960

Copyright

Copyright © 1960 Elsevier Ltd. All rights reserved.

Imprint

Pergamon

Authors

L. FUCHS