By László Fuchs

Written by means of one of many subject’s most well known specialists, this ebook specializes in the crucial advancements and smooth tools of the complicated idea of abelian teams, whereas final obtainable, as an creation and reference, to the non-specialist. It offers a coherent resource for effects scattered through the study literature with plenty of new proofs.

The presentation highlights significant developments that experience appreciably replaced the trendy personality of the topic, specifically, using homological tools within the constitution concept of assorted sessions of abelian teams, and using complex set-theoretical tools within the examine of un decidability difficulties. The therapy of the latter development comprises Shelah’s seminal paintings at the un decidability in ZFC of Whitehead’s challenge; whereas the remedy of the previous development contains an intensive (but non-exhaustive) learn of p-groups, torsion-free teams, combined teams and significant periods of teams bobbing up from ring thought. to arrange the reader to take on those subject matters, the e-book reports the basics of abelian team conception and gives a few historical past fabric from type concept, set concept, topology and homological algebra.

An abundance of routines are integrated to check the reader’s comprehension, and to discover noteworthy extensions and similar sidelines of the most issues. an inventory of open difficulties and questions, in every one bankruptcy, invite the reader to take an lively half within the subject’s extra development.

Show description

Read Online or Download Abelian Groups (Springer Monographs in Mathematics) PDF

Best group theory books

Operational Quantum Theory II: Relativistic Structures: v. 2 (Operational Physics)

Operational Quantum concept II is a unique paintings on quantum concept at a complicated algebraic point. The classically orientated hierarchy with gadgets similar to debris because the basic concentration, and interactions of the gadgets because the secondary concentration is reversed with the operational interactions as uncomplicated quantum constructions.

Structure and Geometry of Lie Groups (Springer Monographs in Mathematics)

This self-contained text is a superb introduction to Lie teams and their activities on manifolds. The authors begin with an elementary discussion of matrix teams, by way of chapters dedicated to the fundamental constitution and illustration conception of finite dimensinal Lie algebras. They then flip to international concerns, demonstrating the major factor of the interaction among differential geometry and Lie concept.

Galois Theory, Coverings, and Riemann Surfaces

The 1st a part of this e-book presents an easy and self-contained exposition of classical Galois thought and its purposes to questions of solvability of algebraic equations in specific shape. the second one half describes a stunning analogy among the elemental theorem of Galois thought and the class of coverings over a topological house.

Representations and Cohomology: Volume 2, Cohomology of Groups and Modules (Cambridge Studies in Advanced Mathematics)

This can be the second one of 2 volumes with a view to supply an advent to trendy advancements within the illustration conception of finite teams and associative algebras. the topic is seen from the point of view of homological algebra and the idea of representations of finite dimensional algebras; the writer emphasises modular representations and the homological algebra linked to their different types.

Additional resources for Abelian Groups (Springer Monographs in Mathematics)

Sample text

Download PDF sample

Rated 4.55 of 5 – based on 4 votes