Infinite Groups And Group Rings
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Infinite Groups And Group Rings
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Author : J M Corson
language : en
Publisher: World Scientific
Release Date : 1993-09-07
Infinite Groups And Group Rings written by J M Corson and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-09-07 with categories.
This proceedings volume consists of contributed papers which deal with diverse topics ranging from logical questions to geometric methods and covering both integral group rings and group algebras. Some papers are research announcements, or of a descriptive nature, while others are research papers. Contents: On Maximal Subgroups of Infinite Groups (J C Beidleman & H Smith)Computer Investigations of Group Algebras (D B Coleman)On HNN-Groups Whose Three-Generator Subgroups are Free (B Fine et al.)Even More Model Theory of Free Groups (A M Gaglione & D Spellman)The Pullback Structure of Blocks with Cyclic Normal Defect Groups (L Klingler & J Haefner)Units of the Integral Group Ring of the Infinite Dihedral Group (F Levin & S Sehgal)The Geometry of PSL(2,Z[ω]) Automorphisms (J Meier)Semiprimitivity of Group Algebras of Locally Finite Groups (D S Passman)The Automorphism Group of a Virtual Direct Product of Groups (M R Pettet)On Infinite Solvable Groups (A Rhemtulla & H Smith)Groups with Triple Factorizations by Abelian Groups (D J S Robinson & S E Stonehewer)A Short Survey on Vertical Heegaard Decompositions of Seifert Fibered Spaces and Nielsen Equivalence in Fuchsian Groups (G Rosenberger & H Terhorst)On the Seventh Lie Dimension Subgroups (K-I Tahara & J Xiao)Aspects of Infinite Symmetric Groups (S Thomas)and other papers Readership: Mathematicians. keywords:Proceedings;Infinite Groups;Group Rings;Tuscaloosa, AL (USA);AMS
Infinite Group Rings
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Author : Donald S. Passman
language : en
Publisher:
Release Date : 1971
Infinite Group Rings written by Donald S. Passman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Mathematics categories.
The algebraic study of group rings was initiated in 1949 by I. Kaplansky. The subject has been pursued by a small but growing number of researchers, and has reached a point in its development where a coherent account of the basic results is needed. That is the goal of this text. The topics covered are selective, with material balanced between ring theory and group theory, and a basic one year course in algebra should provide sufficient background for readers.
Groups Rings And Group Rings
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Author : A. Giambruno
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Groups Rings And Group Rings written by A. Giambruno 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 2009 with Mathematics categories.
Represents the proceedings of the conference on Groups, Rings and Group Rings, held July 28 - August 2, 2008, in Ubatuba, Brazil. This title contains results in active research areas in the theory of groups, group rings and algebras (including noncommutative rings), polynomial identities, Lie algebras and superalgebras.
The Theory Of Infinite Soluble Groups
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Author : John C. Lennox
language : en
Publisher: Clarendon Press
Release Date : 2004-08-19
The Theory Of Infinite Soluble Groups written by John C. Lennox and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-08-19 with Mathematics categories.
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.
Infinite Groups
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Author : Martyn R. Dixon
language : en
Publisher: CRC Press
Release Date : 2022-12-30
Infinite Groups written by Martyn R. Dixon and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-30 with Mathematics categories.
In recent times, group theory has found wider applications in various fields of algebra and mathematics in general. But in order to apply this or that result, you need to know about it, and such results are often diffuse and difficult to locate, necessitating that readers construct an extended search through multiple monographs, articles, and papers. Such readers must wade through the morass of concepts and auxiliary statements that are needed to understand the desired results, while it is initially unclear which of them are really needed and which ones can be dispensed with. A further difficulty that one may encounter might be concerned with the form or language in which a given result is presented. For example, if someone knows the basics of group theory, but does not know the theory of representations, and a group theoretical result is formulated in the language of representation theory, then that person is faced with the problem of translating this result into the language with which they are familiar, etc. Infinite Groups: A Roadmap to Some Classical Areas seeks to overcome this challenge. The book covers a broad swath of the theory of infinite groups, without giving proofs, but with all the concepts and auxiliary results necessary for understanding such results. In other words, this book is an extended directory, or a guide, to some of the more established areas of infinite groups. Features An excellent resource for a subject formerly lacking an accessible and in-depth reference Suitable for graduate students, PhD students, and researchers working in group theory Introduces the reader to the most important methods, ideas, approaches, and constructions in infinite group theory.
Units In Integral Group Rings
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Author : Sudarshan K. Sehgal
language : en
Publisher: Halsted Press
Release Date : 1993-10-01
Units In Integral Group Rings written by Sudarshan K. Sehgal and has been published by Halsted Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-10-01 with categories.
An Introduction To Group Rings
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Author : César Polcino Milies
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-01-31
An Introduction To Group Rings written by César Polcino Milies 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 2002-01-31 with Mathematics categories.
to Group Rings by Cesar Polcino Milies Instituto de Matematica e Estatistica, Universidade de sao Paulo, sao Paulo, Brasil and Sudarshan K. Sehgal Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton. Canada SPRINGER-SCIENCE+BUSINESS MEDIA, B.V. A c.I.P. Catalogue record for this book is available from the Library of Congress. ISBN 978-1-4020-0239-7 ISBN 978-94-010-0405-3 (eBook) DOI 10.1007/978-94-010-0405-3 Printed an acid-free paper AII Rights Reserved (c) 2002 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2002 Softcover reprint ofthe hardcover Ist edition 2002 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, inc1uding photocopying, recording Of by any information storage and retrieval system, without written permis sion from the copyright owner. Contents Preface ix 1 Groups 1 1.1 Basic Concepts . . . . . . . . . . . . 1 1.2 Homomorphisms and Factor Groups 10 1.3 Abelian Groups . 18 1.4 Group Actions, p-groups and Sylow Subgroups 21 1.5 Solvable and Nilpotent Groups 27 1.6 FC Groups .
Unit Groups Of Classical Rings
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Author : Gregory Karpilovsky
language : en
Publisher:
Release Date : 1988
Unit Groups Of Classical Rings written by Gregory Karpilovsky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
The purpose of this book is to give a self-contained, up-to-date account of the structure of unit groups of classical rings. In so doing, the work draws together four areas of mathematics: ring theory, group theory, group representation theory, and algebraic number theory. The ensuing interplay between these disciplines provides a unique source of enrichment for each of them. The main theme centers on two related problems: to determine the isomorphism class of the unit group (U)R of ring R in terms of natural invariants associated with R; and to find an effective method for the construction of units of ring R. Various threads of the development are tied together to convey a comprehensive picture of the current state of the subject. Examples are provided to help research workers who need to compute explicitly unit groups of certain rings. A familiarity with basic ring-theoretic and group-theoretic concepts is assumed, but a chapter on algebraic preliminaries is included. The text is distinguished by its very clear exposition.
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.
Group Identities On Units And Symmetric Units Of Group Rings
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Author : Gregory T Lee
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-19
Group Identities On Units And Symmetric Units Of Group Rings written by Gregory T Lee 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 2010-08-19 with Mathematics categories.
Let FG be the group ring of a group G over a field F. Write U(FG) for the group of units of FG. It is an important problem to determine the conditions under which U(FG) satisfies a group identity. In the mid 1990s, a conjecture of Hartley was verified, namely, if U(FG) satisfies a group identity, and G is torsion, then FG satisfies a polynomial identity. Necessary and sufficient conditions for U(FG) to satisfy a group identity soon followed. Since the late 1990s, many papers have been devoted to the study of the symmetric units; that is, those units u satisfying u* = u, where * is the involution on FG defined by sending each element of G to its inverse. The conditions under which these symmetric units satisfy a group identity have now been determined. This book presents these results for arbitrary group identities, as well as the conditions under which the unit group or the set of symmetric units satisfies several particular group identities of interest.