By L. Fuchs, J. P. Kahane, A. P. Robertson, S. Ulam
Written by way of one of many subject’s preferable specialists, this e-book makes a speciality of the relevant advancements and sleek equipment of the complicated concept of abelian teams, whereas ultimate obtainable, as an creation and reference, to the non-specialist. It presents a coherent resource for effects scattered in the course of the study literature with plenty of new proofs.
The presentation highlights significant tendencies that experience notably replaced the trendy personality of the topic, specifically, using homological tools within the constitution thought of assorted periods of abelian teams, and using complex set-theoretical tools within the learn of un decidability difficulties. The therapy of the latter pattern contains Shelah’s seminal paintings at the un decidability in ZFC of Whitehead’s challenge; whereas the therapy of the previous pattern comprises an in depth (but non-exhaustive) learn of p-groups, torsion-free teams, combined teams and significant sessions of teams coming up from ring conception. to organize the reader to take on those themes, the ebook stories the basics of abelian crew idea and offers a few historical past fabric from class concept, set conception, 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 themes. an inventory of open difficulties and questions, in each one bankruptcy, invite the reader to take an energetic half within the subject’s extra development.
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