Abelian Group Theory
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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.
Exercises In Abelian Group Theory
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Author : D. Valcan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Exercises In Abelian Group Theory written by D. Valcan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
This book, in some sense, began to be written by the first author in 1983, when optional lectures on Abelian groups were held at the Fac ulty of Mathematics and Computer Science,'Babes-Bolyai' University in Cluj-Napoca, Romania. From 1992,these lectures were extended to a twosemester electivecourse on abelian groups for undergraduate stu dents, followed by a twosemester course on the same topic for graduate students in Algebra. All the other authors attended these two years of lectures and are now Assistants to the Chair of Algebra of this Fac ulty. The first draft of this collection, including only exercises solved by students as home works, the last ten years, had 160pages. We felt that there is a need for a book such as this one, because it would provide a nice bridge between introductory Abelian Group Theory and more advanced research problems. The book InfiniteAbelianGroups, published by LaszloFuchsin two volumes 1970 and 1973 willwithout doubt last as the most important guide for abelian group theorists. Many exercises are selected from this source but there are plenty of other bibliographical items (see the Bibliography) which were used in order to make up this collection. For some of the problems stated, recent developments are also given. Nevertheless, there are plenty of elementary results (the so called 'folklore') in Abelian Group Theory whichdo not appear in any written material. It is also one purpose of this book to complete this gap.
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.
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.
Group Theory
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Author : W. R. Scott
language : en
Publisher: Courier Corporation
Release Date : 2012-05-23
Group Theory written by W. R. Scott and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-23 with Mathematics categories.
Here is clear, well-organized coverage of the most standard theorems, including isomorphism theorems, transformations and subgroups, direct sums, abelian groups, and more. This undergraduate-level text features more than 500 exercises.
Abelian Group Theory And Related Topics
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Author : Rüdiger Göbel
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Abelian Group Theory And Related Topics written by Rüdiger Göbel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
This volume contains the proceedings of a conference on abelian groups held in August 1993 at Oberwolfach. The conference brought together forty-seven participants from all over the world and from a range of mathematical areas. Experts from model theory, set theory, noncommutative groups, module theory, and computer science discussed problems in their fields that relate to abelian group theory. This book provides a window on the frontier of this active area of research.
Abelian Groups
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Author : Laszlo Fuchs
language : en
Publisher: CRC Press
Release Date : 2022-01-27
Abelian Groups written by Laszlo Fuchs and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-27 with Mathematics categories.
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 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.
Exercises In Group Theory
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Author : E. Lyapin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Exercises In Group Theory written by E. Lyapin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The present book is a translation of E. S. Lyapin, A. Va. Aizenshtat, and M. M. Lesokhin's Uprazhneniya po teorii grupp. I have departed somewhat from the original text in the following respects. I) I have used Roman letters to indicate sets and their elements, and Greek letters to indicate mappings of sets. The Russian text frequently adopts the opposite usage. 2) I have changed some of the terminology slightly in order to conform with present English usage (e.g., "inverses" instead of "regular conjugates"). 3) I have corrected a number of misprints which appeared in the original in addition to those corrections supplied by Professor Lesokhin. 4) The bibliography has been adapted for readers of English. 5) An index of all defined terms has been compiled (by Anita Zitarelli). 6) I have included a multiplication table for the symmetric group on four elements, which is a frequent source of examples andcounterex::Imples both in this book and in all of group theory. I would like to take this opportunity to thank the authors for their permission to publish this translation. Special thanks are extended to Professor Lesokhin for his errata list and for writing the Foreword to the English Edition. I am particularly indebted to Leo F. Boron, who read the entire manuscript and offered many valuable comments. Finally, to my unerring typists Sandra Rossman and Anita Zitarelli, I am sincerely grateful.
Abelian Groups
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Author : László Fuchs
language : en
Publisher: Springer
Release Date : 2015-12-12
Abelian Groups written by László Fuchs and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-12 with Mathematics categories.
Written by one of the subject’s foremost experts, this book focuses on the central developments and modern methods of the advanced theory of abelian groups, while remaining accessible, as an introduction and reference, to the non-specialist. It provides a coherent source for results scattered throughout the research literature with lots of new proofs. The presentation highlights major trends that have radically changed the modern character of the subject, in particular, the use of homological methods in the structure theory of various classes of abelian groups, and the use of advanced set-theoretical methods in the study of un decidability problems. The treatment of the latter trend includes Shelah’s seminal work on the un decidability in ZFC of Whitehead’s Problem; while the treatment of the former trend includes an extensive (but non-exhaustive) study of p-groups, torsion-free groups, mixed groups and important classes of groups arising from ring theory. To prepare the reader to tackle these topics, the book reviews the fundamentals of abelian group theory and provides some background material from category theory, set theory, topology and homological algebra. An abundance of exercises are included to test the reader’s comprehension, and to explore noteworthy extensions and related sidelines of the main topics. A list of open problems and questions, in each chapter, invite the reader to take an active part in the subject’s further development.