Download or read book The Whitehead Algorithm for free groups written by Chimere Anabanti and published by GRIN Verlag. This book was released on 2015-03-18 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: Master's Thesis from the year 2013 in the subject Mathematics - Algebra, grade: -, University of Warwick (Institute of Mathematics), course: M.Sc dissertation in Pure Mathematics, language: English, abstract: We start with a brief introduction to Free Groups, thereby appreciating Nielsen’s approach to the Subgroup theorem. Beautiful results of J. H. C. Whitehead, J. Nielsen, E. S. Rapaport, Higgins and Lyndon, and J. McCool form our building block. We study different automorphisms of a finitely generated free group as well as a finite set of automorphisms which Whitehead used to deduce that if two elements of a finitely generated free group are equivalent under an automorphism of the group, then they are equivalent under such automorphisms. We write program aimed at appreciating Whitehead’s theorem, starting with programs for appreciating Whitehead automorphisms to programs for determining whether two elements of a finitely generated free group are equivalent or not. We conclude by classifying all minimal words of lengths 2, 3, 4, 5 and 6 in F n (for some n ∈ [2, 6]) up to equivalence.
Download or read book Computational and Experimental Group Theory written by Alexandre Borovik and published by American Mathematical Soc.. This book was released on 2004 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus of algorithmic group theory shifted from the decidability/undecidability type of result to the complexity of algorithms. This title contains papers that reflect that paradigm shift. It presents articles that are based on the AMS/ASL Joint Special Session, Interactions Between Logic, Group Theory and Computer Science.
Download or read book Topics in Infinite Group Theory written by Benjamin Fine and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-08-23 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an advanced overview of several topics in infinite group theory. It can also be considered as a rigorous introduction to combinatorial and geometric group theory. The philosophy of the book is to describe the interaction between these two important parts of infinite group theory. In this line of thought, several theorems are proved multiple times with different methods either purely combinatorial or purely geometric while others are shown by a combination of arguments from both perspectives. The first part of the book deals with Nielsen methods and introduces the reader to results and examples that are helpful to understand the following parts. The second part focuses on covering spaces and fundamental groups, including covering space proofs of group theoretic results. The third part deals with the theory of hyperbolic groups. The subjects are illustrated and described by prominent examples and an outlook on solved and unsolved problems.
Download or read book Geometric Group Theory Down Under written by John Cossey and published by Walter de Gruyter. This book was released on 2011-05-02 with total page 349 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 Discrete Groups and Geometry written by William J. Harvey and published by Cambridge University Press. This book was released on 1992-07-30 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of a conference held at the University of Birmingham to mark the retirement of Professor A. M. Macbeath. The papers represent up-to-date work on a broad spectrum of topics in the theory of discrete group actions, ranging from presentations of finite groups through the detailed study of Fuchsian and crystallographic groups, to applications of group actions in low dimensional topology, complex analysis, algebraic geometry and number theory. For those wishing to pursue research in these areas, this volume offers a valuable summary of contemporary thought and a source of fresh geometric insights.
Download or read book Combinatorial Group Theory and Topology AM 111 Volume 111 written by S. M. Gersten and published by Princeton University Press. This book was released on 2016-03-02 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: Group theory and topology are closely related. The region of their interaction, combining the logical clarity of algebra with the depths of geometric intuition, is the subject of Combinatorial Group Theory and Topology. The work includes papers from a conference held in July 1984 at Alta Lodge, Utah. Contributors to the book include Roger Alperin, Hyman Bass, Max Benson, Joan S. Birman, Andrew J. Casson, Marshall Cohen, Donald J. Collins, Robert Craggs, Michael Dyer, Beno Eckmann, Stephen M. Gersten, Jane Gilman, Robert H. Gilman, Narain D. Gupta, John Hempel, James Howie, Roger Lyndon, Martin Lustig, Lee P. Neuwirth, Andrew J. Nicas, N. Patterson, John G. Ratcliffe, Frank Rimlinger, Caroline Series, John R. Stallings, C. W. Stark, and A. Royce Wolf.
Download or read book Finitely Presented Groups written by Volker Diekert and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-10-07 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains surveys and research articles on the state-of-the-art in finitely presented groups for researchers and graduate students. Overviews of current trends in exponential groups and of the classification of finite triangle groups and finite generalized tetrahedron groups are complemented by new results on a conjecture of Rosenberger and an approximation theorem. A special emphasis is on algorithmic techniques and their complexity, both for finitely generated groups and for finite Z-algebras, including explicit computer calculations highlighting important classical methods. A further chapter surveys connections to mathematical logic, in particular to universal theories of various classes of groups, and contains new results on countable elementary free groups. Applications to cryptography include overviews of techniques based on representations of p-groups and of non-commutative group actions. Further applications of finitely generated groups to topology and artificial intelligence complete the volume. All in all, leading experts provide up-to-date overviews and current trends in combinatorial group theory and its connections to cryptography and other areas.
Download or read book Combinatorial and Geometric Group Theory written by Sean Cleary and published by American Mathematical Soc.. This book was released on 2002 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume grew out of two AMS conferences held at Columbia University (New York, NY) and the Stevens Institute of Technology (Hoboken, NJ) and presents articles on a wide variety of topics in group theory. Readers will find a variety of contributions, including a collection of over 170 open problems in combinatorial group theory, three excellent survey papers (on boundaries of hyperbolic groups, on fixed points of free group automorphisms, and on groups of automorphisms of compactRiemann surfaces), and several original research papers that represent the diversity of current trends in combinatorial and geometric group theory. The book is an excellent reference source for graduate students and research mathematicians interested in various aspects of group theory.
Download or read book Geometric Group Theory written by Ruth Charney and published by Walter de Gruyter. This book was released on 2011-06-24 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thisseries is devoted to the publication of monographs, lecture resp. seminar notes, and other materials arising from programs of the OSU Mathemaical Research Institute. This includes proceedings of conferences or workshops held at the Institute, and other mathematical writings.
Download or read book Contributions to Group Theory written by Kenneth I. Appel and published by American Mathematical Soc.. This book was released on 1984 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains five short articles about Roger Lyndon and his contributions to mathematics, as well as twenty-seven invited research papers in combinatorial group theory and closely related areas. Several of the articles featured in this work fall into subfields of combinatorial group theory, areas in which much of the initial work was done by Lyndon.
Download or read book Geometric Group Theory written by Goulnara N. Arzhantseva and published by Springer Science & Business Media. This book was released on 2007-09-24 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume has its origins in the Barcelona Conference in Group Theory (July 2005) and the conference "Asymptotic and Probabilistic Methods in Geometric Group Theory" held in Geneva (June 2005). Twelve peer-reviewed research articles written by experts in the field present the most recent results in abstract and geometric group theory. In particular there are two articles by A. Juhász.
Download or read book Groups and Computation III written by William M. Kantor and published by Walter de Gruyter. This book was released on 2014-01-02 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains contributions by the participants of the conference "Groups and Computation", which took place at The Ohio State University in Columbus, Ohio, in June 1999. This conference was the successor of two workshops on "Groups and Computation" held at DIMACS in 1991 and 1995. There are papers on permutation group algorithms, finitely presented groups, polycyclic groups, and parallel computation, providing a representative sample of the breadth of Computational Group Theory. On the other hand, more than one third of the papers deal with computations in matrix groups, giving an in-depth treatment of the currently most active area of the field. The points of view of the papers range from explicit computations to group-theoretic algorithms to group-theoretic theorems needed for algorithm development.
Download or read book Combinatorial Methods written by Vladimir Shpilrain and published by Springer Science & Business Media. This book was released on 2012-11-12 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of this book is to show how ideas from combinatorial group theory have spread to two other areas of mathematics: the theory of Lie algebras and affine algebraic geometry. Some of these ideas, in turn, came to combinatorial group theory from low-dimensional topology in the beginning of the 20th Century.
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.
Download or read book Combinatorial Group Theory written by Wilhelm Magnus and published by Courier Corporation. This book was released on 2004-01-01 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: This seminal, much-cited account begins with a fairly elementary exposition of basic concepts and a discussion of factor groups and subgroups. The topics of Nielsen transformations, free and amalgamated products, and commutator calculus receive detailed treatment. The concluding chapter surveys word, conjugacy, and related problems; adjunction and embedding problems; and more. Second, revised 1976 edition.
Download or read book Groups Korea 94 written by A.C. Kim and published by Walter de Gruyter. This book was released on 2011-06-15 with total page 357 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 Geometric Methods in Group Theory written by José Burillo and published by American Mathematical Soc.. This book was released on 2005 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents articles by speakers and participants in two AMS special sessions, Geometric Group Theory and Geometric Methods in Group Theory, held respectively at Northeastern University (Boston, MA) and at Universidad de Sevilla (Spain). The expository and survey articles in the book cover a wide range of topics, making it suitable for researchers and graduate students interested in group theory.
