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Unit Groups Of Group Rings
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Book Synopsis Unit Groups of Classical Rings by : Gregory Karpilovsky
Download or read book Unit Groups of Classical Rings written by Gregory Karpilovsky and published by . This book was released on 1988 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Groups, Rings and Group Rings by : A. Giambruno
Download or read book Groups, Rings and Group Rings written by A. Giambruno and published by American Mathematical Soc.. This book was released on 2009 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author :César Polcino Milies Publisher :Springer Science & Business Media ISBN 13 :9781402002380 Total Pages :394 pages Book Rating :4.0/5 (23 download)
Book Synopsis An Introduction to Group Rings by : César Polcino Milies
Download or read book An Introduction to Group Rings written by César Polcino Milies and published by Springer Science & Business Media. This book was released on 2002-01-31 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 .
Book Synopsis Units in Integral Group Rings by : Sudarshan K. Sehgal
Download or read book Units in Integral Group Rings written by Sudarshan K. Sehgal and published by Halsted Press. This book was released on 1993-10-01 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Unit Groups of Group Rings by : Gregory Karpilovsky
Download or read book Unit Groups of Group Rings written by Gregory Karpilovsky and published by Longman Scientific and Technical. This book was released on 1989 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Group Identities on Units and Symmetric Units of Group Rings by : Gregory T Lee
Download or read book Group Identities on Units and Symmetric Units of Group Rings written by Gregory T Lee and published by Springer Science & Business Media. This book was released on 2010-08-19 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Group Rings and Class Groups by : K.W. Roggenkamp
Download or read book Group Rings and Class Groups written by K.W. Roggenkamp and published by Birkhäuser. This book was released on 2012-12-06 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of the book centers around the isomorphism problem for finite groups; i.e. which properties of the finite group G can be determined by the integral group ring ZZG ? The authors have tried to present the results more or less selfcontained and in as much generality as possible concerning the ring of coefficients. In the first section, the class sum correspondence and some related results are derived. This part is the proof of the subgroup rigidity theorem (Scott - Roggenkamp; Weiss) which says that a finite subgroup of the p-adic integral group ring of a finite p-group is conjugate to a subgroup of the finite group. A counterexample to the conjecture of Zassenhaus that group basis are rationally conjugate, is presented in the semilocal situation (Scott - Roggenkamp). To this end, an extended version of Clifford theory for p-adic integral group rings is presented. Moreover, several examples are given to demonstrate the complexity of the isomorphism problem. The second part of the book is concerned with various aspects of the structure of rings of integers as Galois modules. It begins with a brief overview of major results in the area; thereafter the majority of the text focuses on the use of the theory of Hopf algebras. It begins with a thorough and detailed treatment of the required foundational material and concludes with new and interesting applications to cyclotomic theory and to elliptic curves with complex multiplication. Examples are used throughout both for motivation, and also to illustrate new ideas.
Book Synopsis A First Course in Abstract Algebra by : Marlow Anderson
Download or read book A First Course in Abstract Algebra written by Marlow Anderson and published by CRC Press. This book was released on 2005-01-27 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most abstract algebra texts begin with groups, then proceed to rings and fields. While groups are the logically simplest of the structures, the motivation for studying groups can be somewhat lost on students approaching abstract algebra for the first time. To engage and motivate them, starting with something students know and abstracting from there
Book Synopsis Groups '93 Galway/St Andrews: Volume 2 by : C. M. Campbell
Download or read book Groups '93 Galway/St Andrews: Volume 2 written by C. M. Campbell and published by Cambridge University Press. This book was released on 1995-03-16 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume book contains selected papers from the international conference 'Groups 1993 Galway / St Andrews' which was held at University College Galway in August 1993. The wealth and diversity of group theory is represented in these two volumes. As with the Proceedings of the earlier 'Groups-St Andrews' conferences it is hoped that the articles in these Proceedings will, with their many references, prove valuable both to experienced researchers and also to new postgraduates interested in group theory.
Book Synopsis Group Theory and Computation by : N.S. Narasimha Sastry
Download or read book Group Theory and Computation written by N.S. Narasimha Sastry and published by Springer. This book was released on 2018-09-21 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a blend of recent developments in theoretical and computational aspects of group theory. It presents the state-of-the-art research topics in different aspects of group theory, namely, character theory, representation theory, integral group rings, the Monster simple group, computational algorithms and methods on finite groups, finite loops, periodic groups, Camina groups and generalizations, automorphisms and non-abelian tensor product of groups. Presenting a collection of invited articles by some of the leading and highly active researchers in the theory of finite groups and their representations and the Monster group, with a focus on computational aspects, this book is of particular interest to researchers in the area of group theory and related fields of mathematics.
Book Synopsis Methods in Ring Theory by : Vesselin Drensky
Download or read book Methods in Ring Theory written by Vesselin Drensky and published by CRC Press. This book was released on 1998-03-27 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Furnishes important research papers and results on group algebras and PI-algebras presented recently at the Conference on Methods in Ring Theory held in Levico Terme, Italy-familiarizing researchers with the latest topics, techniques, and methodologies encompassing contemporary algebra."
Book Synopsis Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory by : Gebhard Böckle
Download or read book Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory written by Gebhard Böckle and published by Springer. This book was released on 2018-03-22 with total page 753 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents state-of-the-art research and survey articles that highlight work done within the Priority Program SPP 1489 “Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory”, which was established and generously supported by the German Research Foundation (DFG) from 2010 to 2016. The goal of the program was to substantially advance algorithmic and experimental methods in the aforementioned disciplines, to combine the different methods where necessary, and to apply them to central questions in theory and practice. Of particular concern was the further development of freely available open source computer algebra systems and their interaction in order to create powerful new computational tools that transcend the boundaries of the individual disciplines involved. The book covers a broad range of topics addressing the design and theoretical foundations, implementation and the successful application of algebraic algorithms in order to solve mathematical research problems. It offers a valuable resource for all researchers, from graduate students through established experts, who are interested in the computational aspects of algebra, geometry, and/or number theory.
Book Synopsis Infinite Groups 1994 by : Francesco Giovanni
Download or read book Infinite Groups 1994 written by Francesco Giovanni and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-03-06 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Download or read book Groups - Korea 1983 written by A.C. Kim and published by Springer. This book was released on 2006-12-08 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Course in Finite Group Representation Theory by : Peter Webb
Download or read book A Course in Finite Group Representation Theory written by Peter Webb and published by Cambridge University Press. This book was released on 2016-08-19 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer characters, and block theory. This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader's knowledge, provide further examples and practice, and include results not proven in the text. Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.
Book Synopsis Representation Theory, Group Rings, and Coding Theory by : M. Isaacs
Download or read book Representation Theory, Group Rings, and Coding Theory written by M. Isaacs and published by American Mathematical Soc.. This book was released on 1989 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to the memory of the Soviet mathematician S. D. Berman (1922-1987). Berman's work - for the most part in representation theory, group rings, and coding theory - is discussed here in a number of review articles. Among the topics covered are Berman's achievements in coding theory, including his pioneering work on abelian codes and his results on the theory of threshold functions. Also discussed are his contributions to the representation theory of groups over fields, his work on integral representations of groups, his accomplishments in infinite abelian group rings, and his fundamental results on units in integral group rings. In addition, there are 22 research articles written by an international group of researchers in areas of Berman's major interest.
Book Synopsis Proceedings of the Conference on Orders, Group Rings and Related Topics by : J. S. Hsia
Download or read book Proceedings of the Conference on Orders, Group Rings and Related Topics written by J. S. Hsia and published by Springer. This book was released on 2006-11-15 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt:
