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Author : G. Moran
Publisher :
ISBN 13 :
Total Pages : 34 pages
Book Rating : 4.:/5 (897 download)
Download or read book The Products of Conjugacy Classes in Some Infinite Simple Groups written by G. Moran and published by . This book was released on 1983 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Zvi Arad
Publisher : Springer
ISBN 13 : 3540391428
Total Pages : 249 pages
Book Rating : 4.5/5 (43 download)
Download or read book Products of Conjugacy Classes in Groups written by Zvi Arad and published by Springer. This book was released on 2006-11-14 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Graham Higman
Publisher :
ISBN 13 :
Total Pages : 96 pages
Book Rating : 4.3/5 (91 download)
Download or read book Finitely Presented Infinite Simple Groups written by Graham Higman and published by . This book was released on 1974 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Piotr Antosik
Publisher :
ISBN 13 : 9780387139166
Total Pages : 244 pages
Book Rating : 4.1/5 (391 download)
Download or read book Products of Conjugacy Classes in Groups written by Piotr Antosik and published by . This book was released on 1985 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Mario Curzio
Publisher :
ISBN 13 :
Total Pages : 360 pages
Book Rating : 4.3/5 (91 download)
Download or read book Topics in Infinite Groups written by Mario Curzio and published by . This book was released on 2001 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : B. Hartley
Publisher : Springer Science & Business Media
ISBN 13 : 9401103291
Total Pages : 469 pages
Book Rating : 4.4/5 (11 download)
Download or read book Finite and Locally Finite Groups written by B. Hartley and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the NATO Advanced Study Institute on Finite and Locally Finite Groups held in Istanbul, Turkey, 14-27 August 1994, at which there were about 90 participants from some 16 different countries. The ASI received generous financial support from the Scientific Affairs Division of NATO. INTRODUCTION A locally finite group is a group in which every finite set of elements is contained in a finite subgroup. The study of locally finite groups began with Schur's result that a periodic linear group is, in fact, locally finite. The simple locally finite groups are of particular interest. In view of the classification of the finite simple groups and advances in representation theory, it is natural to pursue classification theorems for simple locally finite groups. This was one of the central themes of the Istanbul conference and significant progress is reported herein. The theory of simple locally finite groups intersects many areas of group theory and representation theory, so this served as a focus for several articles in the volume. Every simple locally finite group has what is known as a Kegel cover. This is a collection of pairs {(G , Ni) liE I}, where I is an index set, each group Gi is finite, i Ni
Author : Antonio Machì
Publisher : Springer Science & Business Media
ISBN 13 : 8847024218
Total Pages : 385 pages
Book Rating : 4.8/5 (47 download)
Download or read book Groups written by Antonio Machì and published by Springer Science & Business Media. This book was released on 2012-04-05 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: Groups are a means of classification, via the group action on a set, but also the object of a classification. How many groups of a given type are there, and how can they be described? Hölder’s program for attacking this problem in the case of finite groups is a sort of leitmotiv throughout the text. Infinite groups are also considered, with particular attention to logical and decision problems. Abelian, nilpotent and solvable groups are studied both in the finite and infinite case. Permutation groups and are treated in detail; their relationship with Galois theory is often taken into account. The last two chapters deal with the representation theory of finite group and the cohomology theory of groups; the latter with special emphasis on the extension problem. The sections are followed by exercises; hints to the solution are given, and for most of them a complete solution is provided.
Author : Dipl.-Math. Felix F. Flemisch
Publisher : BoD – Books on Demand
ISBN 13 : 3758333202
Total Pages : 69 pages
Book Rating : 4.7/5 (583 download)
Download or read book The Strong Sylow Theorem for the Prime p in Simple Locally Finite Groups written by Dipl.-Math. Felix F. Flemisch and published by BoD – Books on Demand. This book was released on 2024-04-10 with total page 69 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research paper continues [15]. We begin with giving a profound overview of the structure of arbitrary simple groups and in particular of the simple locally finite groups and reduce their Sylow theory for the prime p to a quite famous conjecture by Prof. Otto H. Kegel (see [37], Theorem 2.4: "Let the p-subgroup P be a p-uniqueness subgroup in the finite simple group S which belongs to one of the seven rank-unbounded families. Then the rank of S is bounded in terms of P.") about the rank-unbounded ones of the 19 known families of finite simple groups. We introduce a new scheme to describe the 19 families, the family T of types, define the rank of each type, and emphasise the rôle of Kegel covers. This part presents a unified picture of known results whose proofs are by reference. Subsequently we apply new ideas to prove the conjecture for the alternating groups. Thereupon we are remembering Kegel covers and *-sequences. Next we suggest a way 1) and a way 2) how to prove and even how to optimise Kegel's conjecture step-by-step or peu à peu which leads to Conjecture 1, Conjecture 2 and Conjecture 3 thereby unifying Sylow theory in locally finite simple groups with Sylow theory in locally finite and p-soluble groups whose joint study directs Sylow theory in (locally) finite groups. For any unexplained terminology we refer to [15]. We then continue the program begun above to optimise along the way 1) the theorem about the first type "An" of infinite families of finite simple groups step-by-step to further types by proving it for the second type "A = PSLn". We start with proving Conjecture 2 about the General Linear Groups over (commutative) locally finite fields, stating that their rank is bounded in terms of their p-uniqueness, and then break down this insight to the Special Linear Groups and the Projective Special Linear (PSL) Groups over locally finite fields. We close with suggestions for future research -> regarding the remaining rank-unbounded types (the "Classical Groups") and the way 2), -> regarding (locally) finite and p-soluble groups, and -> regarding Cauchy's and Galois' contributions to Sylow theory in finite groups. We much hope to enthuse group theorists with them. We include the predecessor research paper [15] as an Appendix.
Author : R.W. Carter
Publisher : Springer Science & Business Media
ISBN 13 : 9401153086
Total Pages : 388 pages
Book Rating : 4.4/5 (11 download)
Download or read book Algebraic Groups and their Representations written by R.W. Carter and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains 19 articles written by speakers at the Advanced Study Institute on 'Modular representations and subgroup structure of al gebraic groups and related finite groups' held at the Isaac Newton Institute, Cambridge from 23rd June to 4th July 1997. We acknowledge with gratitude the financial support given by the NATO Science Committee to enable this ASI to take place. Generous financial support was also provided by the European Union. We are also pleased to acknowledge funds given by EPSRC to the Newton Institute which were used to support the meeting. It is a pleasure to thank the Director of the Isaac Newton Institute, Professor Keith Moffatt, and the staff of the Institute for their dedicated work which did so much to further the success of the meeting. The editors wish to thank Dr. Ross Lawther and Dr. Nick Inglis most warmly for their help in the production of this volume. Dr. Lawther in particular made an invaluable contribution in preparing the volume for submission to the publishers. Finally we wish to thank the distinguished speakers at the ASI who agreed to write articles for this volume based on their lectures at the meet ing. We hope that the volume will stimulate further significant advances in the theory of algebraic groups.
Author : Jack Koolen
Publisher : CRC Press
ISBN 13 : 0203885767
Total Pages : 188 pages
Book Rating : 4.2/5 (38 download)
Download or read book Applications of Group Theory to Combinatorics written by Jack Koolen and published by CRC Press. This book was released on 2008-07-02 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applications of Group Theory to Combinatorics contains 11 survey papers from international experts in combinatorics, group theory and combinatorial topology. The contributions cover topics from quite a diverse spectrum, such as design theory, Belyi functions, group theory, transitive graphs, regular maps, and Hurwitz problems, and present the state
Author : Larry Finkelstein, William M. Kantor
Publisher : American Mathematical Soc.
ISBN 13 : 9780821885772
Total Pages : 404 pages
Book Rating : 4.8/5 (857 download)
Download or read book Groups and Computation II written by Larry Finkelstein, William M. Kantor and published by American Mathematical Soc.. This book was released on with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: The workshop "Groups and Computations" took place at the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS) at Rutgers University in June 1995. This and an earlier workshop held in October 1991 was aimed at merging theory and practice within the broad area of computation with groups. The primary goal of the previous workshop was to foster a dialogue between researchers studying the computational complexity of group algorithms and those engaged in the development of practical software. It was expected that this would lead to a deeper understanding of the mathematical issues underlying group computation and that this understanding would lead, in turn, to faster algorithms. Comments and subsequent work indicated that this goal had been achieved beyond expectations. The second workshop was designed to reinforce the progress in these directions. The scientific program consisted of invited lectures and research announcements, as well as informal discussions and software demonstrations. The eight extended talks discussed randomization, permutation groups, matrix groups, software systems, fast Fourier transforms and their applications to signal processing and data analysis, computations with finitely presented groups, and implementation and complexity questions. As in the previous workshop, speakers ranged from established researchers to graduate students.
Author : Su Gao
Publisher : American Mathematical Soc.
ISBN 13 : 1470418479
Total Pages : 254 pages
Book Rating : 4.4/5 (74 download)
Download or read book Group Colorings and Bernoulli Subflows written by Su Gao and published by American Mathematical Soc.. This book was released on 2016-04-26 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the authors study the dynamics of Bernoulli flows and their subflows over general countable groups. One of the main themes of this paper is to establish the correspondence between the topological and the symbolic perspectives. From the topological perspective, the authors are particularly interested in free subflows (subflows in which every point has trivial stabilizer), minimal subflows, disjointness of subflows, and the problem of classifying subflows up to topological conjugacy. Their main tool to study free subflows will be the notion of hyper aperiodic points; a point is hyper aperiodic if the closure of its orbit is a free subflow.
Author : Anil Kumar
Publisher : BFC Publications
ISBN 13 : 9356329532
Total Pages : 315 pages
Book Rating : 4.3/5 (563 download)
Download or read book Basic Group Theory written by Anil Kumar and published by BFC Publications. This book was released on 2023-05-17 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on Group theory for undergraduate students (Mathematics), Scholarship test (NBHM, TIFR, JEST), JRF/LS(CSIR-UGC-NET), M.Sc. entrance test (IIT-JAM), Ph.D. admission entrance test (IIT-GATE), Aspirants of Civil Services examinations (UPSC-CSE and IFS, State PCs), DRDO examinations etc. In this book all the topics of group theory are discussed with theory and suitable examples. The book is divided into eight chapters viz. groups, subgroups, normal subgroups, homomorphism, direct products in group theory, Sylow`s theorems, group actions and finite groups. All chapters containing solved examples, solution of previous years question papers of different competitive examinations UPSC(CSE), UPSC(IFS), NBHM, CSIR-UGC-NET, GATE, BPSC, IIT-JAM and exercises.
Author : Derek J.S. Robinson
Publisher : Springer Science & Business Media
ISBN 13 : 1441985948
Total Pages : 518 pages
Book Rating : 4.4/5 (419 download)
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
Author : Manfred Droste
Publisher : Springer
ISBN 13 : 331951718X
Total Pages : 493 pages
Book Rating : 4.3/5 (195 download)
Download or read book Groups, Modules, and Model Theory - Surveys and Recent Developments written by Manfred Droste and published by Springer. This book was released on 2017-06-02 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume focuses on group theory and model theory with a particular emphasis on the interplay of the two areas. The survey papers provide an overview of the developments across group, module, and model theory while the research papers present the most recent study in those same areas. With introductory sections that make the topics easily accessible to students, the papers in this volume will appeal to beginning graduate students and experienced researchers alike. As a whole, this book offers a cross-section view of the areas in group, module, and model theory, covering topics such as DP-minimal groups, Abelian groups, countable 1-transitive trees, and module approximations. The papers in this book are the proceedings of the conference “New Pathways between Group Theory and Model Theory,” which took place February 1-4, 2016, in Mülheim an der Ruhr, Germany, in honor of the editors’ colleague Rüdiger Göbel. This publication is dedicated to Professor Göbel, who passed away in 2014. He was one of the leading experts in Abelian group theory.
Author : Francesco Giovanni
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110810387
Total Pages : 356 pages
Book Rating : 4.1/5 (18 download)
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.
Author : Martyn R. Dixon
Publisher : CRC Press
ISBN 13 : 1000848310
Total Pages : 411 pages
Book Rating : 4.0/5 (8 download)
Download or read book Infinite Groups written by Martyn R. Dixon and published by CRC Press. This book was released on 2022-12-30 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
