Infinite Abelian Group Theory
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Infinite Abelian Group Theory
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Author : Phillip A. Griffith
language : en
Publisher:
Release Date : 1970
Infinite Abelian Group Theory written by Phillip A. Griffith and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Abelian groups categories.
Infinite Abelian Groups
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Author :
language : en
Publisher: Academic Press
Release Date : 1970-01-01
Infinite Abelian Groups written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970-01-01 with Mathematics categories.
Infinite Abelian Groups
Infinite Abelian Groups
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Author : Irving Kaplansky
language : en
Publisher: Courier Dover Publications
Release Date : 2018-12-18
Infinite Abelian Groups written by Irving Kaplansky and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-18 with Mathematics categories.
In the Introduction to this concise monograph, the author states his two main goals: first, "to make the theory of infinite abelian groups available in a convenient form to the mathematical public; second, to help students acquire some of the techniques used in modern infinite algebra." Suitable for advanced undergraduates and graduate students in mathematics, the text requires no extensive background beyond the rudiments of group theory. Starting with examples of abelian groups, the treatment explores torsion groups, Zorn's lemma, divisible groups, pure subgroups, groups of bounded order, and direct sums of cyclic groups. Subsequent chapters examine Ulm's theorem, modules and linear transformations, Banach spaces, valuation rings, torsion-free and complete modules, algebraic compactness, characteristic submodules, and the ring of endomorphisms. Many exercises appear throughout the book, along with a guide to the literature and a detailed bibliography.
The Theory Of Infinite Soluble Groups
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Author : John C. Lennox
language : en
Publisher: Clarendon Press
Release Date : 2004-08-19
The Theory Of Infinite Soluble Groups written by John C. Lennox and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-08-19 with Mathematics categories.
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 Group Theory
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Author : Rüdiger Göbel
language : en
Publisher: CRC Press
Release Date : 1987
Abelian Group Theory written by Rüdiger Göbel and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.
Aspects Of Infinite Groups
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Author : Benjamin Fine
language : en
Publisher: World Scientific
Release Date : 2008
Aspects Of Infinite Groups written by Benjamin Fine and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
This book is a festschrift in honor of Professor Anthony Gaglione''s sixtieth birthday. This volume presents an excellent mix of research and expository articles on various aspects of infinite group theory. The papers give a broad overview of present research in infinite group theory in general, and combinatorial group theory and non-Abelian group-based cryptography in particular. They also pinpoint the interactions between combinatorial group theory and mathematical logic, especially model theory.
Abelian Groups
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Author : L. Fuchs
language : en
Publisher: Elsevier
Release Date : 2014-07-15
Abelian Groups written by L. Fuchs and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-15 with Mathematics categories.
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.
Infinite Group Theory From The Past To The Future
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Author : Fine Benjamin
language : en
Publisher: World Scientific
Release Date : 2017-12-26
Infinite Group Theory From The Past To The Future written by Fine Benjamin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-26 with Mathematics categories.
The development of algebraic geometry over groups, geometric group theory and group-based cryptography, has led to there being a tremendous recent interest in infinite group theory. This volume presents a good collection of papers detailing areas of current interest. Contents: Groups with the Weak Minimal Condition on Non-Permutable Subgroups (Laxmi K Chatuat and Martyn R Dixon)A Survey: Shamir Threshold Scheme and Its Enhancements (Chi Sing Chum, Benjamin Fine, and Xiaowen Zhang)The Zappa-Szep Product of Left-Orderable Groups (Fabienne Chouraqui)Totally Disconnected Groups From Baumslag-Solitar Groups (Murray Elder and George Willis)Elementary and Universal Theories of Nonabelian Commutative Transitive and CSA Groups (B Fine, A M Gaglione, and D Spellman)Commutative Transitivity and the CSA Property (Benjamin Fine, Anthony Gaglione, Gerhard Rosenberger, and Dennis Spellman)The Universal Theory of Free Burnside Groups of Large Prime Exponent (Anthony M Gaglione, Seymour Lipschutz, and Dennis Spellman)Primitive Curve Lengths on Pairs of Pants (Jane Gilman)Drawing Inferences Under Maximum Entropy From Relational Probabilistic Knowledge Using Group Theory (Gabriele Kern-Isberner, Marco Wilhelm, and Christoph Beierle)On Some Infinite-Dimensional Linear Groups and the Structure of Related Modules (L A Kurdachenko and I Ya Subbotin)On New Analogs of Some Classical Group Theoretical Results in Lie Rings (L A Kurdachenko, A A Pypka and I Ya Subbotin)Log-Space Complexity of the Conjugacy Problem in Wreath Products (Alexei Myasnikov, Svetla Vassileva, and Armin Weiss)Group Presentations, Cayley Graphs and Markov Processes (Peter Olszewski) Readership: Graduate students and researchers in group theory. Keywords: Infinite Group Theory;Combinatorial Group Theory;Geometric Group TheoryReview: Key Features: This book is centered on infinite group theory from a combinatorial and geometric point of view. It also contains material on non-commutative algebraic group-based cryptography
Abelian Group Theory
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Author : R. Göbel
language : de
Publisher: Springer-Verlag
Release Date : 2006-11-14
Abelian Group Theory written by R. Göbel and has been published by Springer-Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Abelian Groups
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Author : Carol Jacoby
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2019-07-22
Abelian Groups written by Carol Jacoby and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-22 with Mathematics categories.
This monograph covers in a comprehensive manner the current state of classification theory with respect to infinite abelian groups. A wide variety of ways to characterise different classes of abelian groups by invariants, isomorphisms and duality principles are discussed.