Polycyclic Groups
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Polycyclic Groups
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Author : Daniel Segal
language : en
Publisher: Cambridge University Press
Release Date : 2005-11-17
Polycyclic Groups written by Daniel Segal and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-17 with Mathematics categories.
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.
Three Lectures On Polycyclic Groups
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Author : J. E. Roseblade
language : en
Publisher:
Release Date : 1973
Three Lectures On Polycyclic Groups written by J. E. Roseblade and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Group rings categories.
Group And Ring Theoretic Properties Of Polycyclic Groups
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Author : B.A.F. Wehrfritz
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-11-28
Group And Ring Theoretic Properties Of Polycyclic Groups written by B.A.F. Wehrfritz 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 2009-11-28 with Mathematics categories.
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.
Three Lectures On Polycyclic Groups
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Author :
language : en
Publisher:
Release Date : 1970
Three Lectures On Polycyclic Groups written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Polycyclic groups categories.
Group And Ring Theoretic Properties Of Polycyclic Groups
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Author : B. A. F. Wehrfritz
language : en
Publisher:
Release Date : 2010-04-17
Group And Ring Theoretic Properties Of Polycyclic Groups written by B. A. F. Wehrfritz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-17 with categories.
Central Extensions Of Polycyclic Groups
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Author : Werner Nickel
language : en
Publisher:
Release Date : 1993
Central Extensions Of Polycyclic Groups written by Werner Nickel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Polycyclic groups categories.
Exercises In Cellular Automata And Groups
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Author : Tullio Ceccherini-Silberstein
language : en
Publisher: Springer Nature
Release Date : 2023-11-01
Exercises In Cellular Automata And Groups written by Tullio Ceccherini-Silberstein and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-01 with Mathematics categories.
This book complements the authors’ monograph Cellular Automata and Groups [CAG] (Springer Monographs in Mathematics). It consists of more than 600 fully solved exercises in symbolic dynamics and geometric group theory with connections to geometry and topology, ring and module theory, automata theory and theoretical computer science. Each solution is detailed and entirely self-contained, in the sense that it only requires a standard undergraduate-level background in abstract algebra and general topology, together with results established in [CAG] and in previous exercises. It includes a wealth of gradually worked out examples and counterexamples presented here for the first time in textbook form. Additional comments provide some historical and bibliographical information, including an account of related recent developments and suggestions for further reading. The eight-chapter division from [CAG] is maintained. Each chapter begins with a summary of the main definitions and results contained in the corresponding chapter of [CAG]. The book is suitable either for classroom or individual use. Foreword by Rostislav I. Grigorchuk
The Santa Cruz Conference On Finite Groups
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Author : Bruce Cooperstein
language : en
Publisher: American Mathematical Soc.
Release Date : 1980
The Santa Cruz Conference On Finite Groups written by Bruce Cooperstein 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 1980 with Mathematics categories.
Computation With Finitely Presented Groups
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Author : Charles C. Sims
language : en
Publisher: Cambridge University Press
Release Date : 1994-01-28
Computation With Finitely Presented Groups written by Charles C. Sims and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-01-28 with Mathematics categories.
Research in computational group theory, an active subfield of computational algebra, has emphasised three areas: finite permutation groups, finite solvable groups, and finitely presented groups. This book deals with the third of these areas. The author emphasises the connections with fundamental algorithms from theoretical computer science, particularly the theory of automata and formal languages, computational number theory, and computational commutative algebra. The LLL lattice reduction algorithm and various algorithms for Hermite and Smith normal forms from computational number theory are used to study the abelian quotients of a finitely presented group. The work of Baumslag, Cannonito and Miller on computing nonabelian polycyclic quotients is described as a generalisation of Buchberger's Gröbner basis methods to right ideals in the integral group ring of a polycyclic group. Researchers in computational group theory, mathematicians interested in finitely presented groups and theoretical computer scientists will find this book useful.
Fundamentals Of The Theory Of Groups
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Author : M. I. Kargapolov
language : en
Publisher: Springer
Release Date : 1979-12-20
Fundamentals Of The Theory Of Groups written by M. I. Kargapolov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979-12-20 with Mathematics categories.
The present edition differs from the first in several places. In particular our treatment of polycyclic and locally polycyclic groups-the most natural generalizations of the classical concept of a finite soluble group-has been expanded. We thank Ju. M. Gorcakov, V. A. Curkin and V. P. Sunkov for many useful remarks. The Authors Novosibirsk, Akademgorodok, January 14, 1976. v Preface to the First Edition This book consists of notes from lectures given by the authors at Novosi birsk University from 1968 to 1970. Our intention was to set forth just the fundamentals of group theory, avoiding excessive detail and skirting the quagmire of generalizations (however a few generalizations are nonetheless considered-see the last sections of Chapters 6 and 7). We hope that the student desiring to work in the theory of groups, having become acquainted with its fundamentals from these notes, will quickly be able to proceed to the specialist literature on his chosen topic. We have striven not to cross the boundary between abstract and scholastic group theory, elucidating difficult concepts by means of simple examples wherever possible. Four types of examples accompany the theory: numbers under addition, numbers under multiplication, permutations, and matrices.
