By László Fuchs
Written by means of one of many subject’s ultimate specialists, this publication makes a speciality of the principal advancements and glossy tools of the complicated conception of abelian teams, whereas last obtainable, as an creation and reference, to the non-specialist. It presents a coherent resource for effects scattered through the examine literature with plenty of new proofs.
The presentation highlights significant tendencies that experience significantly replaced the fashionable personality of the topic, specifically, using homological equipment within the constitution concept of varied periods of abelian teams, and using complicated set-theoretical tools within the research of un decidability difficulties. The remedy of the latter pattern contains Shelah’s seminal paintings at the un decidability in ZFC of Whitehead’s challenge; whereas the remedy of the previous pattern comprises an in depth (but non-exhaustive) examine of p-groups, torsion-free teams, combined teams and significant periods of teams coming up from ring conception. to organize the reader to take on those subject matters, the publication experiences the basics of abelian team idea and gives a few historical past fabric from class concept, set idea, topology and homological algebra.
An abundance of routines are integrated to check the reader’s comprehension, and to discover noteworthy extensions and comparable sidelines of the most issues. a listing of open difficulties and questions, in each one bankruptcy, invite the reader to take an lively half within the subject’s additional development.
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Abelian Groups (Springer Monographs in Mathematics) by László Fuchs