Download or read book Group Algebras of Torsion Free Poycyclic Groups and Relation Modules of Finite Groups written by P. A. Linnell and published by . This book was released on 1979 with total page 85 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Relation Modules of Finite Groups written by Karl W. Gruenberg and published by American Mathematical Soc.. This book was released on 1976 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Polycyclic Groups written by Daniel Segal and published by Cambridge University Press. This book was released on 2005-11-17 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of polycyclic groups is a branch of infinite group theory which has a rather different flavour from the rest of that subject. This book is a comprehensive account of the present state of this theory. As well as providing a connected and self-contained account of the group-theoretical background, it explains in detail how deep methods of number theory and algebraic group theory have been used to achieve some very recent and rather spectacular advances in the subject. Up to now, most of this material has only been available in scattered research journals, and some of it is new. This book is the only unified account of these developments, and will be of interest to mathematicians doing research in algebra, and to postgraduate students studying that subject.
Download or read book Group and Ring Theoretic Properties of Polycyclic Groups written by B.A.F. Wehrfritz and published by Springer Science & Business Media. This book was released on 2009-11-28 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Polycyclic groups are built from cyclic groups in a specific way. They arise in many contexts within group theory itself but also more generally in algebra, for example in the theory of Noetherian rings. The first half of this book develops the standard group theoretic techniques for studying polycyclic groups and the basic properties of these groups. The second half then focuses specifically on the ring theoretic properties of polycyclic groups and their applications, often to purely group theoretic situations. The book is intended to be a study manual for graduate students and researchers coming into contact with polycyclic groups, where the main lines of the subject can be learned from scratch. Thus it has been kept short and readable with a view that it can be read and worked through from cover to cover. At the end of each topic covered there is a description without proofs, but with full references, of further developments in the area. An extensive bibliography then concludes the book.
Download or read book Groups with Prescribed Quotient Groups and Associated Module Theory written by L. Kurdachenko and published by World Scientific. This book was released on 2002 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Finite Groups written by Bertram A. F. Wehrfritz and published by World Scientific. This book was released on 1999 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of groups, especially of finite groups, is one of the most delightful areas of mathematics. Its proofs often have elegance and crystalline beauty. This textbook is intended for the reader who has been exposed to about three years of serious mathematics. The notion of a group appears widely in mathematics and even further afield in physics and chemistry, and the fundamental idea should be known to all mathematicians. In this textbook a purely algebraic approach is taken and the choice of material is based upon the notion of conjugacy. The aim is not only to cover basic material, but also to present group theory as a living, vibrant and growing discipline, by including references and discussion of some work up to the present day.
Download or read book Three Lectures on Polycyclic Groups written by J. E. Roseblade and published by . This book was released on 1973 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Group Algebras and Their Modules written by P. Landrock and published by Cambridge University Press. This book was released on 1983-12-29 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with the structure of group algebras of finite groups over fields of characteristic [lowercase italic]p dividing the order of the group, or closely related rings such as rings of algebraic integers and in particular their [lowercase italic]p-adic completions, as well as modules and homomorphisms between them, or such group algebras. Our principal aim has been to present some of the more recent ideas which have enriched and improved this theory. This text is not restricted to particular methods, be they ring theoretic or character theoretic, while presenting approaches or proofs which are distinguished by being fast, elegant, illuminating, with potential for further advancement, or all of these at the same time. This text hopes to attract non-specialists, perhaps algebraic topologists and group theorists who might use the tools of modular representations more frequently.
Download or read book Algebra IV written by A.I. Kostrikin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Course in the Theory of Groups written by Derek J.S. Robinson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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
Download or read book Finiteness Conditions and Generalized Soluble Groups written by Derek J.S. Robinson and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a study of group theoretical properties of two disparate kinds, firstly finiteness conditions or generalizations of finiteness and secondly generalizations of solubility or nilpotence. It will be particularly interesting to discuss groups which possess properties of both types. The origins of the subject may be traced back to the nineteen twenties and thirties and are associated with the names of R. Baer, S.N. Cernikov, K.A. Hirsch, A.G. Kuros, 0.]. Schmidt and H. Wielandt. Since this early period, the body of theory has expanded at an increasingly rapid rate through the efforts of many group theorists, particularly in Germany, Great Britain and the Soviet Union. Some of the highest points attained can, perhaps, be found in the work of P. Hall and A.I. Mal'cev on infinite soluble groups. Kuras's well-known book "The theory of groups" has exercised a strong influence on the development of the theory of infinite groups: this is particularly true of the second edition in its English translation of 1955. To cope with the enormous increase in knowledge since that date, a third volume, containing a survey of the contents of a very large number of papers but without proofs, was added to the book in 1967
Download or read book Seminar on Algebraic Groups and Related Finite Groups written by Armand Borel and published by Springer. This book was released on 2006-11-14 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Proceedings of the Conference on Finite Groups written by William R. Scott and published by Academic Press. This book was released on 2014-05-10 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the Conference on Finite Groups provides information pertinent to the fundamental aspects of finite group theory. This book presents the problem of characterizing simple groups in terms of the local structure of a group. Organized into five parts encompassing 43 chapters, this book begins with an overview of the characterization of the Chevalley groups over fields of odd order and indicates the role of this characterization in the theory of component type groups. This text then examines the structure as well as the representations of specific simple groups. Other chapters consider the general theory of representations and characters of finite groups. This book discusses as well permutation groups and the connection between group theory and geometry. The final chapter deals with finite solvable groups as well as the theory of formations. This book is a valuable resource for mathematicians, graduate students, and research workers.
Download or read book Finite Groups II written by B. Huppert and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: 17):~t? L It CIFDr- ! wei! unsre Weisheit Einfalt ist, From "Lohengrin", Richard Wagner At the time of the appearance of the first volume of this work in 1967, the tempestuous development of finite group theory had already made it virtually impossible to give a complete presentation of the subject in one treatise. The present volume and its successor have therefore the more modest aim of giving descriptions of the recent development of certain important parts of the subject, and even in these parts no attempt at completeness has been made. Chapter VII deals with the representation theory of finite groups in arbitrary fields with particular attention to those of non-zero charac teristic. That part of modular representation theory which is essentially the block theory of complex characters has not been included, as there are already monographs on this subject and others will shortly appear. Instead, we have restricted ourselves to such results as can be obtained by purely module-theoretical means.
Download or read book Skew Linear Groups written by M. Shirvani and published by Cambridge University Press. This book was released on 1986 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with subgroups of groups of the form GL(n,D) for some division ring D. In it the authors bring together many of the advances in the theory of skew linear groups. Some aspects of skew linear groups are similar to those for linear groups, however there are often significant differences either in the method of proof or the results themselves. Topics covered in this volume include irreducibility, unipotence, locally finite-dimensional division algebras, and division algebras associated with polycyclic groups. Both authors are experts in this area of current interest in group theory, and algebraists and research students will find this an accessible account of the subject.
Download or read book The Theory of Nilpotent Groups written by Anthony E. Clement and published by Birkhäuser. This book was released on 2017-11-18 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents both classical and recent results in the theory of nilpotent groups and provides a self-contained, comprehensive reference on the topic. While the theorems and proofs included can be found throughout the existing literature, this is the first book to collect them in a single volume. Details omitted from the original sources, along with additional computations and explanations, have been added to foster a stronger understanding of the theory of nilpotent groups and the techniques commonly used to study them. Topics discussed include collection processes, normal forms and embeddings, isolators, extraction of roots, P-localization, dimension subgroups and Lie algebras, decision problems, and nilpotent groups of automorphisms. Requiring only a strong undergraduate or beginning graduate background in algebra, graduate students and researchers in mathematics will find The Theory of Nilpotent Groups to be a valuable resource.
Download or read book Group Theory written by Karl W. Gruenberg and published by . This book was released on 1984 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume celebrates the major impact on modern group theory made by Philip Hall. The survey articles were commissioned to provide reasonably self-contained, up-to-date and forward-looking accounts of finite and infinite group theory. Mathematicians working on group theory and ring theory will find this volume interesting and useful, and the material is accessible to students specializing in algebra. This book was prepared for Philip Hall's 80th birthday, but is now published after his death as a tribute to his genius. FROM THE PREFACE: This book was to have been an eightieth birthday present for Philip Hall. In the summer of 1980 the Council of the London Mathematical Society asked us to edit a volume to mark Hall's 80th birthday on the eleventh of April 1984. We decided to produce a book in two parts: the first to consist of commissioned survey articles and the second of submitted research papers. Because we intended to invite research articles by advertisement, we had to tell Hall something of our plans; this we did at a pub lunch outside Cambridge in May 1981. At the same time we asked him if he would agree to take part in a birthday celebration in his honour which had been proposed by the Society. Characteristically he said that he would prefer no public festivity; but he liked the idea of a book, especially the surveys. Our idea was that each survey would give a reasonably self-contained, up-to-date and forward-looking account of an area in which Hall had made important contributions. In view of Hall's considerable impact on modern group theory, we hoped that the essays would together form a fairly coherent picture of the subject. So as to avoid too much overlap, we suggested to each author the area we should like him to cover, but only in broad terms; the choice of material within the suggested area was left entirely to him. It was inevitable, perhaps, that gaps would remain. When Hall died on 30th December 1982, we felt that the second half of the planned book was no longer appropriate, but that the essays should still be published. We offer them here not as a memorial volume, since they were largely written while Philip Hall was alive and well, but as a tribute to his genius.
