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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.
This volume focuses on group theory and model theory with a
particular emphasis on the interplay of the two areas. The survey
papers provide an overview of the developments across group,
module, and model theory while the research papers present the most
recent study in those same areas. With introductory sections that
make the topics easily accessible to students, the papers in this
volume will appeal to beginning graduate students and experienced
researchers alike. As a whole, this book offers a cross-section
view of the areas in group, module, and model theory, covering
topics such as DP-minimal groups, Abelian groups, countable
1-transitive trees, and module approximations. The papers in this
book are the proceedings of the conference "New Pathways between
Group Theory and Model Theory," which took place February 1-4,
2016, in Mulheim an der Ruhr, Germany, in honor of the editors'
colleague Rudiger Goebel. This publication is dedicated to
Professor Goebel, who passed away in 2014. He was one of the
leading experts in Abelian group theory.
This volume contains information offered at the international
conference held in Curacao, Netherlands Antilles. It presents the
latest developments in the most active areas of abelian groups,
particularly in torsion-free abelian groups.;For both researchers
and graduate students, it reflects the current status of abelian
group theory.;Abelian Groups discusses: finite rank Butler groups;
almost completely decomposable groups; Butler groups of infinite
rank; equivalence theorems for torsion-free groups; cotorsion
groups; endomorphism algebras; and interactions of set theory and
abelian groups.;This volume contains contributions from
international experts. It is aimed at algebraists and logicians,
research mathematicians, and advanced graduate students in these
disciplines.
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.
This volume focuses on group theory and model theory with a
particular emphasis on the interplay of the two areas. The survey
papers provide an overview of the developments across group,
module, and model theory while the research papers present the most
recent study in those same areas. With introductory sections that
make the topics easily accessible to students, the papers in this
volume will appeal to beginning graduate students and experienced
researchers alike. As a whole, this book offers a cross-section
view of the areas in group, module, and model theory, covering
topics such as DP-minimal groups, Abelian groups, countable
1-transitive trees, and module approximations. The papers in this
book are the proceedings of the conference "New Pathways between
Group Theory and Model Theory," which took place February 1-4,
2016, in Mulheim an der Ruhr, Germany, in honor of the editors'
colleague Rudiger Goebel. This publication is dedicated to
Professor Goebel, who passed away in 2014. He was one of the
leading experts in Abelian group theory.
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