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 un decidability
problems. The treatment of the latter trend includes Shelah's
seminal work on the un decidability 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.
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