Unit Groups Of Group Rings
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| Author | : Donald S. Passman |
| Publisher | : Courier Corporation |
| Total Pages | : 754 |
| Release | : 2011-01-01 |
| Genre | : Mathematics |
| ISBN | : 0486482065 |
"'Highly recommended' by the Bulletin of the London Mathematical Society, this book offers a comprehensive, self-contained treatment of group rings. The subject involves the intersection of two essentially different disciplines, group theory and ring theory. The Bulletin of the American Mathematical Society hailed this treatment as 'a majestic account,' proclaiming it "encyclopedic and lucid." 1985 edition"--
| Author | : César Polcino Milies |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 394 |
| Release | : 2002-01-31 |
| Genre | : Mathematics |
| ISBN | : 9781402002380 |
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 .
| Author | : Gregory Karpilovsky |
| Publisher | : Longman Scientific and Technical |
| Total Pages | : 418 |
| Release | : 1989 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : Gregory T Lee |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 198 |
| Release | : 2010-08-19 |
| Genre | : Mathematics |
| ISBN | : 1849965048 |
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.
| Author | : Alberto Facchini |
| Publisher | : CRC Press |
| Total Pages | : |
| Release | : 2018-09-18 |
| Genre | : |
| ISBN | : 9781138401839 |
Rings, Modules, Algebras, and Abelian Groups summarizes the proceedings of a recent algebraic conference held at Venice International University in Italy. Surveying the most influential developments in the field, this reference reviews the latest research on Abelian groups, algebras and their representations, module and ring theory, and topological algebraic structures, and provides more than 600 current references and 570 display equations for further exploration of the topic. It provides stimulating discussions from world-renowned names including Laszlo Fuchs, Robert Gilmer, Saharon Shelah, Daniel Simson, and Richard Swan to celebrate 40 years of study on cumulative rings. Describing emerging theories
| Author | : Sudarshan K. Sehgal |
| Publisher | : Halsted Press |
| Total Pages | : 357 |
| Release | : 1993-10-01 |
| Genre | : |
| ISBN | : 9780470200087 |
| Author | : Marlow Anderson |
| Publisher | : CRC Press |
| Total Pages | : 684 |
| Release | : 2005-01-27 |
| Genre | : Mathematics |
| ISBN | : 1420057111 |
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
| Author | : Eric Jespers |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 228 |
| Release | : 2015-11-13 |
| Genre | : Mathematics |
| ISBN | : 3110411504 |
This two-volume graduate textbook gives a comprehensive, state-of-the-art account of describing large subgroups of the unit group of the integral group ring of a finite group and, more generally, of the unit group of an order in a finite dimensional semisimple rational algebra. Since the book is addressed to graduate students as well as young researchers, all required background on these diverse areas, both old and new, is included. Supporting problems illustrate the results and complete some of the proofs. Volume 1 contains all the details on describing generic constructions of units and the subgroup they generate. Volume 2 mainly is about structure theorems and geometric methods. Without being encyclopaedic, all main results and techniques used to achieve these results are included. Basic courses in group theory, ring theory and field theory are assumed as background.
| Author | : Craig Huneke |
| Publisher | : Cambridge University Press |
| Total Pages | : 446 |
| Release | : 2006-10-12 |
| Genre | : Mathematics |
| ISBN | : 0521688604 |
Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.
| Author | : Sudarshan K. Sehgal |
| Publisher | : |
| Total Pages | : 272 |
| Release | : 1978 |
| Genre | : Mathematics |
| ISBN | : |
The group ring KG of the group G over a commutative unital ring K comprises an attractive object of study. This is one of the few algebraic structures that allow for explicit computations. Several easily formulated questions are associated with this topic. Many interesting results have been obtained in this area by using deep results and techniques from group theory, ring theory, and number theory. Most of the results presented and techniques used have a number theoretic flavor. Aimed at advanced graduate students and research mathematicians in algebra.
