By László Fuchs
Written by means of one of many subject’s most appropriate specialists, this booklet specializes in the important advancements and sleek equipment of the complex concept of abelian teams, whereas closing available, as an creation and reference, to the non-specialist. It presents a coherent resource for effects scattered during the study literature with plenty of new proofs.
The presentation highlights significant developments that experience substantially replaced the trendy personality of the topic, specifically, using homological equipment within the constitution conception of assorted periods of abelian teams, and using complicated set-theoretical tools within the examine of un decidability difficulties. The therapy of the latter development contains Shelah’s seminal paintings at the un decidability in ZFC of Whitehead’s challenge; whereas the remedy of the previous pattern comprises an intensive (but non-exhaustive) learn of p-groups, torsion-free teams, combined teams and critical periods of teams bobbing up from ring conception. to arrange the reader to take on those issues, the publication experiences the basics of abelian crew thought and gives a few history fabric from type thought, set concept, topology and homological algebra.
An abundance of workouts are integrated to check the reader’s comprehension, and to discover noteworthy extensions and similar sidelines of the most issues. a listing of open difficulties and questions, in every one bankruptcy, invite the reader to take an energetic half within the subject’s additional development.
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Abelian Groups (Springer Monographs in Mathematics) by László Fuchs