Abelian Groups

  • László Fuchs

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xxi
  2. László Fuchs
    Pages 1-41
  3. László Fuchs
    Pages 43-74
  4. László Fuchs
    Pages 75-129
  5. László Fuchs
    Pages 131-148
  6. László Fuchs
    Pages 149-181
  7. László Fuchs
    Pages 183-212
  8. László Fuchs
    Pages 213-228
  9. László Fuchs
    Pages 229-253
  10. László Fuchs
    Pages 255-298
  11. László Fuchs
    Pages 299-342
  12. László Fuchs
    Pages 343-408
  13. László Fuchs
    Pages 409-479
  14. László Fuchs
    Pages 481-528
  15. László Fuchs
    Pages 529-572
  16. László Fuchs
    Pages 573-612
  17. László Fuchs
    Pages 613-653
  18. László Fuchs
    Pages 655-671
  19. László Fuchs
    Pages 673-706
  20. Back Matter
    Pages 707-747

About this book


Written by one of the subject’s foremost experts, this book focuses on the central developments and modern methods of the advanced theory of abelian groups, while remaining accessible, as an introduction and reference, to the non-specialist. It provides a coherent source for results scattered throughout the research literature with lots of new proofs.

The presentation highlights major trends that have radically changed the modern character of the subject, in particular, the use of homological methods in the structure theory of various classes of abelian groups, and the use of advanced set-theoretical methods in the study of undecidability problems. The treatment of the latter trend includes Shelah’s seminal work on the undecidability in ZFC of Whitehead’s Problem; while the treatment of the former trend includes an extensive (but non-exhaustive) study of p-groups, torsion-free groups, mixed groups, and important classes of groups arising from ring theory. To prepare the reader to tackle these topics, the book reviews the fundamentals of abelian group theory and provides some background material from category theory, set theory, topology, and homological algebra.

An abundance of exercises are included to test the reader’s comprehension, and to explore noteworthy extensions and related sidelines of the main topics. A list of open problems and questions, in each chapter, invite the reader to take an active part in the subject’s further development.


Butler group abelian group automorphism group endomorphism ring homomorphism groups torsion

Authors and affiliations

  • László Fuchs
    • 1
  1. 1.Mathematics DepartmentTulane UniversityNew OrleansUSA

Bibliographic information