Infinite Abelian Groups

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Editor: Academic Press
ISBN: 9780080873480
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Infinite Abelian Groups

Infinite Abelian Groups

Author: Irving Kaplansky
Editor: Courier Dover Publications
ISBN: 0486828506
File Size: 33,47 MB
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This concise monograph presents the theory of infinite abelian groups in a convenient form and helps students acquire some of the techniques used in modern infinite algebra. 1969 edition.

Infinite Abelian Groups

Author: László Fuchs
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ISBN:
File Size: 18,98 MB
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Infinite Abelian Group Theory

Author: Phillip A. Griffith
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ISBN: 9780226308708
File Size: 46,76 MB
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Classifying Some Infinite Abelian Groups And Answering Kaplansky S Test Questions

Author: Alexander F. Shaw
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In his influential title Infinite Abelian Groups, Irving Kaplansky posed two general questions designed to test classifications of abelian groups. This work answers the questions for a subclass of abelian p-groups that are entirely characterized by their socles (the subgroups with 0 and all elements of order p). The socle is generalized as a valuated vector space and much of this work is dedicated to classifying this generalization in terms of Ulm invariants. For these groups, the questions can thus be translated in two steps: first into the terms of socles and then into the terms of Ulm invariants. The first step is made by Fuchs and Irwin in [1]. This work makes the second step, building up the results and classifications while assuming only working knowledge of introductory algebra. In culmination, this work answers Kaplansky's test questions and gives an example to which the results apply.

The Complete Independence Of A Set Of Postulates For Infinite Abelian Groups Due To Huntington

Author: Ruth Estelle Brant
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ISBN:
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Infinite Groups 1994

Author: Francesco Giovanni
Editor: Walter de Gruyter GmbH & Co KG
ISBN: 3110810387
File Size: 29,22 MB
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The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

Abelian Groups And Modules

Author: Paul C. Eklof
Editor: Springer Science & Business Media
ISBN: 9783764361723
File Size: 45,77 MB
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This volume contains the refereed proceedings of the International Conference on Abelian Groups and Modules held at the Dublin Institute of Technology in Ireland, from August 10 until August 14, 1998. The meeting brought together more than 50 researchers and graduate students from 14 countries around the world. In a series of eight invited survey talks, experts in the field presented several active areas of research, including:· Almost completely decomposable abelian groups, Butler groups and almost free groups nbsp;â the classification problem, and invariants of special classes of torsion-free abelian groups.· Totally projective groups, their automorphism groups and their group rings â questions about unique passage between these categories.· Radicals commuting with products.· The Ziegler spectra of Neumann regular rings and the class (semi-) groups of PrÃ1⁄4fer domains.· The Krull-Schmidt property for valuation domains.These main talks were accompanied by many other presentations of current research on abelian groups and modules. Methods from model theory, category theory, infinite combinatorics, representation theory, classical algebra and geometry were applied to the study of abelian groups and modules; conversely, results and methods from abelian group theory were applied to general module theory and non-commutative groups.All this is reflected in the 30 articles in this volume, which introduce the reader to an active and attractive part of algebra that over the years has gained much from its position at the crossroads of mathematics. Lively discussions at the conference influenced the final work on the presented papers, which convey some sense of the intellectual ferment they generated and stimulate the reader to consider and actively investigate the topics and problems contained therein.

Infinite Linear Groups

Author: Bertram Wehrfritz
Editor: Springer Science & Business Media
ISBN: 3642870813
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By a linear group we mean essentially a group of invertible matrices with entries in some commutative field. A phenomenon of the last twenty years or so has been the increasing use of properties of infinite linear groups in the theory of (abstract) groups, although the story of infinite linear groups as such goes back to the early years of this century with the work of Burnside and Schur particularly. Infinite linear groups arise in group theory in a number of contexts. One of the most common is via the automorphism groups of certain types of abelian groups, such as free abelian groups of finite rank, torsion-free abelian groups of finite rank and divisible abelian p-groups of finite rank. Following pioneering work of Mal'cev many authors have studied soluble groups satisfying various rank restrictions and their automor phism groups in this way, and properties of infinite linear groups now play the central role in the theory of these groups. It has recently been realized that the automorphism groups of certain finitely generated soluble (in particular finitely generated metabelian) groups contain significant factors isomorphic to groups of automorphisms of finitely generated modules over certain commutative Noetherian rings. The results of our Chapter 13, which studies such groups of automorphisms, can be used to give much information here.

Proceedings Of The Special Semester On Infinite Abelian Groups

Author: Stephen Murphrey
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File Size: 78,50 MB
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Enumeration Theorems In Infinite Abelian Groups

Author: Delmar L. Boyer
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Abelian Groups

Author: L. Fuchs
Editor: Elsevier
ISBN: 148328090X
File Size: 63,52 MB
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Abelian Groups deals with the theory of abelian or commutative groups, with special emphasis on results concerning structure problems. More than 500 exercises of varying degrees of difficulty, with and without hints, are included. Some of the exercises illuminate the theorems cited in the text by providing alternative developments, proofs or counterexamples of generalizations. Comprised of 16 chapters, this volume begins with an overview of the basic facts on group theory such as factor group or homomorphism. The discussion then turns to direct sums of cyclic groups, divisible groups, and direct summands and pure subgroups, as well as Kulikov's basic subgroups. Subsequent chapters focus on the structure theory of the three main classes of abelian groups: the primary groups, the torsion-free groups, and the mixed groups. Applications of the theory are also considered, along with other topics such as homomorphism groups and endomorphism rings; the Schreier extension theory with a discussion of the group of extensions and the structure of the tensor product. In addition, the book examines the theory of the additive group of rings and the multiplicative group of fields, along with Baer's theory of the lattice of subgroups. This book is intended for young research workers and students who intend to familiarize themselves with abelian groups.

Abelian Groups

Author: Laszlo Fuchs
Editor: CRC Press
ISBN: 9780824789015
File Size: 53,38 MB
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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.

Abelian Groups And Representations Of Finite Partially Ordered Sets

Author: David Arnold
Editor: Springer Science & Business Media
ISBN: 1441987509
File Size: 73,18 MB
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The theme of this book is an exposition of connections between representations of finite partially ordered sets and abelian groups. Emphasis is placed throughout on classification, a description of the objects up to isomorphism, and computation of representation type, a measure of when classification is feasible. David M. Arnold is the Ralph and Jean Storm Professor of Mathematics at Baylor University. He is the author of "Finite Rank Torsion Free Abelian Groups and Rings" published in the Springer-Verlag Lecture Notes in Mathematics series, a co-editor for two volumes of conference proceedings, and the author of numerous articles in mathematical research journals.

The Theory Of Infinite Soluble Groups

Author: John C. Lennox
Editor: Clarendon Press
ISBN: 9780191523151
File Size: 16,23 MB
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The central concept in this monograph is that of a soluble group - a group which is built up from abelian groups by repeatedly forming group extensions. It covers all the major areas, including finitely generated soluble groups, soluble groups of finite rank, modules over group rings, algorithmic problems, applications of cohomology, and finitely presented groups, whilst remaining fairly strictly within the boundaries of soluble group theory. An up-to-date survey of the area aimed at research students and academic algebraists and group theorists, it is a compendium of information that will be especially useful as a reference work for researchers in the field.

Abelian Groups

Author: László Fuchs
Editor:
ISBN:
File Size: 66,65 MB
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Representation Theory Group Rings And Coding Theory

Author: M. Isaacs
Editor: American Mathematical Soc.
ISBN: 0821850989
File Size: 47,70 MB
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This volume is dedicated to the memory of the Soviet mathematician S. D. Berman (1922-1987). Berman's work - for the most part in representation theory, group rings, and coding theory - is discussed here in a number of review articles. Among the topics covered are Berman's achievements in coding theory, including his pioneering work on abelian codes and his results on the theory of threshold functions. Also discussed are his contributions to the representation theory of groups over fields, his work on integral representations of groups, his accomplishments in infinite abelian group rings, and his fundamental results on units in integral group rings. In addition, there are 22 research articles written by an international group of researchers in areas of Berman's major interest.

Algebra Iv

Author: A.I. Kostrikin
Editor: Springer Science & Business Media
ISBN: 3662028697
File Size: 45,21 MB
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Group theory is one of the most fundamental branches of mathematics. This highly accessible volume of the Encyclopaedia is devoted to two important subjects within this theory. Extremely useful to all mathematicians, physicists and other scientists, including graduate students who use group theory in their work.

A Course In The Theory Of Groups

Author: Derek J.S. Robinson
Editor: Springer Science & Business Media
ISBN: 1441985948
File Size: 69,29 MB
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"An excellent up-to-date introduction to the theory of groups. It is general yet comprehensive, covering various branches of group theory. The 15 chapters contain the following main topics: free groups and presentations, free products, decompositions, Abelian groups, finite permutation groups, representations of groups, finite and infinite soluble groups, group extensions, generalizations of nilpotent and soluble groups, finiteness properties." —-ACTA SCIENTIARUM MATHEMATICARUM