Exercises In Abelian Group Theory
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| Author | : D. Valcan |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 353 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 9401703396 |
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.
| Author | : László Fuchs |
| Publisher | : Springer |
| Total Pages | : 762 |
| Release | : 2015-12-12 |
| Genre | : Mathematics |
| ISBN | : 3319194224 |
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.
| Author | : E. Lyapin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 245 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461345898 |
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.
| Author | : John D. Dixon |
| Publisher | : Courier Corporation |
| Total Pages | : 194 |
| Release | : 2007-01-01 |
| Genre | : Mathematics |
| ISBN | : 0486459160 |
265 challenging problems in all phases of group theory, gathered for the most part from papers published since 1950, although some classics are included.
| Author | : Dino Lorenzini |
| Publisher | : American Mathematical Society |
| Total Pages | : 397 |
| Release | : 2021-12-23 |
| Genre | : Mathematics |
| ISBN | : 1470467259 |
Extremely carefully written, masterfully thought out, and skillfully arranged introduction … to the arithmetic of algebraic curves, on the one hand, and to the algebro-geometric aspects of number theory, on the other hand. … an excellent guide for beginners in arithmetic geometry, just as an interesting reference and methodical inspiration for teachers of the subject … a highly welcome addition to the existing literature. —Zentralblatt MATH The interaction between number theory and algebraic geometry has been especially fruitful. In this volume, the author gives a unified presentation of some of the basic tools and concepts in number theory, commutative algebra, and algebraic geometry, and for the first time in a book at this level, brings out the deep analogies between them. The geometric viewpoint is stressed throughout the book. Extensive examples are given to illustrate each new concept, and many interesting exercises are given at the end of each chapter. Most of the important results in the one-dimensional case are proved, including Bombieri's proof of the Riemann Hypothesis for curves over a finite field. While the book is not intended to be an introduction to schemes, the author indicates how many of the geometric notions introduced in the book relate to schemes, which will aid the reader who goes to the next level of this rich subject.
| Author | : J. F. Humphreys |
| Publisher | : Oxford University Press, USA |
| Total Pages | : 296 |
| Release | : 1996 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 9780198534594 |
Each chapter ends with a summary of the material covered and notes on the history and development of group theory.
| Author | : Bao Luong |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 167 |
| Release | : 2009-08-14 |
| Genre | : Mathematics |
| ISBN | : 0817649166 |
This unified, self-contained book examines the mathematical tools used for decomposing and analyzing functions, specifically, the application of the [discrete] Fourier transform to finite Abelian groups. With countless examples and unique exercise sets at the end of each section, Fourier Analysis on Finite Abelian Groups is a perfect companion to a first course in Fourier analysis. This text introduces mathematics students to subjects that are within their reach, but it also has powerful applications that may appeal to advanced researchers and mathematicians. The only prerequisites necessary are group theory, linear algebra, and complex analysis.
| Author | : Antonio Machì |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 385 |
| Release | : 2012-04-05 |
| Genre | : Mathematics |
| ISBN | : 8847024218 |
Groups are a means of classification, via the group action on a set, but also the object of a classification. How many groups of a given type are there, and how can they be described? Hölder’s program for attacking this problem in the case of finite groups is a sort of leitmotiv throughout the text. Infinite groups are also considered, with particular attention to logical and decision problems. Abelian, nilpotent and solvable groups are studied both in the finite and infinite case. Permutation groups and are treated in detail; their relationship with Galois theory is often taken into account. The last two chapters deal with the representation theory of finite group and the cohomology theory of groups; the latter with special emphasis on the extension problem. The sections are followed by exercises; hints to the solution are given, and for most of them a complete solution is provided.
| Author | : D. Valcan |
| Publisher | : Springer |
| Total Pages | : 351 |
| Release | : 2013-01-11 |
| Genre | : Mathematics |
| ISBN | : 9789401703406 |
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.
| Author | : H.E. Rose |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 314 |
| Release | : 2009-12-16 |
| Genre | : Mathematics |
| ISBN | : 1848828896 |
Introduces the richness of group theory to advanced undergraduate and graduate students, concentrating on the finite aspects. Provides a wealth of exercises and problems to support self-study. Additional online resources on more challenging and more specialised topics can be used as extension material for courses, or for further independent study.
