Groups With Prescribed Quotient Groups And Associated Module Theory
Groups With Prescribed Quotient Groups And Associated Module Theory Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Groups With Prescribed Quotient Groups And Associated Module Theory book. This book definitely worth reading, it is an incredibly well-written.
Groups with Prescribed Quotient Groups and Associated Module Theory by L. Kurdachenko,Jean-Pierre Otal,I. Subbotin Pdf
Presents well-established results as well as newer, contemporary achievements in this area from the common integral point of view. This view is based on the implementation of module theory for solving group problems.
Algebra and Number Theory by Martyn R. Dixon,Leonid A. Kurdachenko,Igor Ya Subbotin Pdf
Explore the main algebraic structures and number systems that play a central role across the field of mathematics Algebra and number theory are two powerful branches of modern mathematics at the forefront of current mathematical research, and each plays an increasingly significant role in different branches of mathematics, from geometry and topology to computing and communications. Based on the authors' extensive experience within the field, Algebra and Number Theory has an innovative approach that integrates three disciplines—linear algebra, abstract algebra, and number theory—into one comprehensive and fluid presentation, facilitating a deeper understanding of the topic and improving readers' retention of the main concepts. The book begins with an introduction to the elements of set theory. Next, the authors discuss matrices, determinants, and elements of field theory, including preliminary information related to integers and complex numbers. Subsequent chapters explore key ideas relating to linear algebra such as vector spaces, linear mapping, and bilinear forms. The book explores the development of the main ideas of algebraic structures and concludes with applications of algebraic ideas to number theory. Interesting applications are provided throughout to demonstrate the relevance of the discussed concepts. In addition, chapter exercises allow readers to test their comprehension of the presented material. Algebra and Number Theory is an excellent book for courses on linear algebra, abstract algebra, and number theory at the upper-undergraduate level. It is also a valuable reference for researchers working in different fields of mathematics, computer science, and engineering as well as for individuals preparing for a career in mathematics education.
The Theory of Infinite Soluble Groups by John C. Lennox,Derek J. S. Robinson Pdf
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.
Linear Groups by Martyn R. Dixon,Leonid A. Kurdachenko,Igor Ya. Subbotin Pdf
Linear Groups: The Accent on Infinite Dimensionality explores some of the main results and ideas in the study of infinite-dimensional linear groups. The theory of finite dimensional linear groups is one of the best developed algebraic theories. The array of articles devoted to this topic is enormous, and there are many monographs concerned with matrix groups, ranging from old, classical texts to ones published more recently. However, in the case when the dimension is infinite (and such cases arise quite often), the reality is quite different. The situation with the study of infinite dimensional linear groups is like the situation that has developed in the theory of groups, in the transition from the study of finite groups to the study of infinite groups which appeared about one hundred years ago. It is well known that this transition was extremely efficient and led to the development of a rich and central branch of algebra: Infinite group theory. The hope is that this book can be part of a similar transition in the field of linear groups. Features This is the first book dedicated to infinite-dimensional linear groups This is written for experts and graduate students specializing in algebra and parallel disciplines This book discusses a very new theory and accumulates many important and useful results
Ischia Group Theory 2010 by Mariagrazia Bianchi,Mariagrazia Bianchi Oddera,Patrizia Longobardi,Mercede Maj Pdf
The papers in this volume represent the proceedings of the Conference entitled "Ischia Group Theory 2010," which took place at NH Ischia Thermal SPA Resort, Ischia, Naples, Italy, from April 14 to April 17, 2010. The articles in this volume are contributions by speakers and participants of the Conference. The volume contains a collection of research articles by leading experts in group theory and some accessible surveys of recent research in the area. Together they provide an overview of the diversity of themes and applications that interest group theorists today. Topics covered in this volume include: finite p-groups, character and representation theory, combinatorial group theory, varieties of groups, profinite and pro-p-groups, linear groups, graphs connected with groups, subgroup structure, finiteness conditions, radical rings, conjugacy classes, automorphisms.
Artinian Modules over Group Rings by Leonid Kurdachenko,Javier Otal,Igor Ya Subbotin Pdf
This book highlights important developments on artinian modules over group rings of generalized nilpotent groups. Along with traditional topics such as direct decompositions of artinian modules, criteria of complementability for some important modules, and criteria of semisimplicity of artinian modules, it also focuses on recent advanced results on these matters.
Ranks of Groups by Martyn R. Dixon,Leonid A. Kurdachenko,Igor Ya Subbotin Pdf
A comprehensive guide to ranks and group theory Ranks of Groups features a logical, straightforward presentation, beginning with a succinct discussion of the standard ranks before moving on to specific aspects of ranks of groups. Topics covered include section ranks, groups of finite 0-rank, minimax rank, special rank, groups of finite section p-rank, groups having finite section p-rank for all primes p, groups of finite bounded section rank, groups whose abelian subgroups have finite rank, groups whose abelian subgroups have bounded finite rank, finitely generated groups having finite rank, residual properties of groups of finite rank, groups covered by normal subgroups of bounded finite rank, and theorems of Schur and Baer. This book presents fundamental concepts and notions related to the area of ranks in groups. Class-tested worldwide by highly qualified authors in the fields of abstract algebra and group theory, this book focuses on critical concepts with the most interesting, striking, and central results. In order to provide readers with the most useful techniques related to the various different ranks in a group, the authors have carefully examined hundreds of current research articles on group theory authored by researchers around the world, providing an up-to-date, comprehensive treatment of the subject. • All material has been thoroughly vetted and class-tested by well-known researchers who have worked in the area of rank conditions in groups • Topical coverage reflects the most modern, up-to-date research on ranks of groups • Features a unified point-of-view on the most important results in ranks obtained using various methods so as to illustrate the role those ranks play within group theory • Focuses on the tools and methods concerning ranks necessary to achieve significant progress in the study and clarification of the structure of groups Ranks of Groups: The Tools, Characteristics, and Restrictions is an excellent textbook for graduate courses in mathematics, featuring numerous exercises, whose solutions are provided. This book will be an indispensable resource for mathematicians and researchers specializing in group theory and abstract algebra. MARTYN R. DIXON, PhD, is Professor in the Department of Mathematics at the University of Alabama. LEONID A. KURDACHENKO, PhD, DrS, is Distinguished Professor and Chair of the Department of Algebra at the University of Dnepropetrovsk, Ukraine. IGOR YA SUBBOTIN, PhD, is Professor in the Department of Mathematics and Natural Sciences at National University in Los Angeles, California.
C. M. Campbell,M. R. Quick,E. F. Robertson,C. M. Roney-Dougal,G. C. Smith,G. Traustason
Author : C. M. Campbell,M. R. Quick,E. F. Robertson,C. M. Roney-Dougal,G. C. Smith,G. Traustason Publisher : Cambridge University Press Page : 310 pages File Size : 54,5 Mb Release : 2011-06-16 Category : Mathematics ISBN : 9781139498272
Groups St Andrews 2009 in Bath: Volume 1 by C. M. Campbell,M. R. Quick,E. F. Robertson,C. M. Roney-Dougal,G. C. Smith,G. Traustason Pdf
This first volume of a two-volume book contains selected papers from the international conference Groups St Andrews 2009. Leading researchers in their respective areas, including Gerhard Hiss and Volodymyr Nekrashevych, survey the latest developments in algebra.
Rings Related to Stable Range Conditions by Huanyin Chen Pdf
This monograph is concerned with exchange rings in various conditions related to stable range. Diagonal reduction of regular matrices and cleanness of square matrices are also discussed. Readers will come across various topics: cancellation of modules, comparability of modules, cleanness, monoid theory, matrix theory, K-theory, topology, amongst others. This is a first-ever book that contains many of these topics considered under stable range conditions. It will be of great interest to researchers and graduate students involved in ring and module theories. Contents:Stable Range OneUnit 1-Stable RangeOn m-Fold Stable RingsStrongly Stable RingsWeakly Stable RingsRelated ComparabilityGeneralized Stable RingsQB-RingsPB-RingsPower-CancellationStably Euclidean RingsThe n-Stable Range ConditionStable Range for IdealsDiagonal ReductionClean Properties, IClean Properties, IIAbelian Rings and Exchange Readership: Mathematicians and graduate students interested in ring and module theory. Keywords:Associative Ring;Exchange Ring;Clean Ring;Regular Ring;Stable Range Conditions;ModuleKey Features:An original book that encompasses recent developments of the fieldA reference text which gives a general introduction to the theory of a ring with various element-wise characterizationsA valuable resource for researchers and graduate students who wish to know the most recent progress in ring theory
Ring Constructions and Applications by Andrei V. Kelarev Pdf
This book contains the definitions of several ring constructions used in various applications. The concept of a groupoid-graded ring includes many of these constructions as special cases and makes it possible to unify the exposition. Recent research results on groupoid-graded rings and more specialized constructions are presented. In addition, there is a chapter containing open problems currently considered in the literature. Ring Constructions and Applications can serve as an excellent introduction for graduate students to many ring constructions as well as to essential basic concepts of group, semigroup and ring theories used in proofs.
