Computation With Finitely Presented Groups
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Computation with Finitely Presented Groups
Author | : Charles C. Sims |
Publsiher | : Cambridge University Press |
Total Pages | : 624 |
Release | : 1994-01-28 |
Genre | : Mathematics |
ISBN | : 9780521432139 |
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Research in computational group theory, an active subfield of computational algebra, has emphasised three areas: finite permutation groups, finite solvable groups, and finitely presented groups. This book deals with the third of these areas. The author emphasises the connections with fundamental algorithms from theoretical computer science, particularly the theory of automata and formal languages, computational number theory, and computational commutative algebra. The LLL lattice reduction algorithm and various algorithms for Hermite and Smith normal forms from computational number theory are used to study the abelian quotients of a finitely presented group. The work of Baumslag, Cannonito and Miller on computing nonabelian polycyclic quotients is described as a generalisation of Buchberger's Gröbner basis methods to right ideals in the integral group ring of a polycyclic group. Researchers in computational group theory, mathematicians interested in finitely presented groups and theoretical computer scientists will find this book useful.
Handbook of Computational Group Theory
Author | : Derek F. Holt,Bettina Eick,Eamonn A. O'Brien |
Publsiher | : CRC Press |
Total Pages | : 532 |
Release | : 2005-01-13 |
Genre | : Mathematics |
ISBN | : 9781420035216 |
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The origins of computation group theory (CGT) date back to the late 19th and early 20th centuries. Since then, the field has flourished, particularly during the past 30 to 40 years, and today it remains a lively and active branch of mathematics. The Handbook of Computational Group Theory offers the first complete treatment of all the fundame
Varieties of Representations of Finitely Generated Groups
Author | : Alexander Lubotzky,Andy R. Magid |
Publsiher | : American Mathematical Soc. |
Total Pages | : 117 |
Release | : 1985 |
Genre | : Mathematics |
ISBN | : 9780821823378 |
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Groups and Computation III
Author | : William M. Kantor,Ákos Seress |
Publsiher | : Walter de Gruyter |
Total Pages | : 376 |
Release | : 2014-01-02 |
Genre | : Mathematics |
ISBN | : 9783110872743 |
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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.
Groups and Computation II
Author | : Larry Finkelstein, William M. Kantor |
Publsiher | : American Mathematical Soc. |
Total Pages | : 404 |
Release | : 2024 |
Genre | : Algebra |
ISBN | : 0821885774 |
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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.
Computational Support for Discrete Mathematics
Author | : Nathaniel Dean,Gregory E. Shannon |
Publsiher | : American Mathematical Soc. |
Total Pages | : 416 |
Release | : 2024 |
Genre | : Mathematics |
ISBN | : 0821870610 |
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With recent technological advances in workstations, graphics, graphical user interfaces, and object oriented programming languages, a significant number of researchers are developing general-purpose software and integrated software systems for domains in discrete mathematics, including graph theory, combinatorics, combinatorial optimization, and sets. This software aims to provide effective computational tools for research, applications prototyping, and teaching. In March 1992, DIMACS sponsored a workshop on Computational Support for Discrete Mathematics in order to facilitate interactions between the researchers, developers, and educators who work in these areas. Containing refereed papers based on talks presented at the workshop, this volume documents current and past research in these areas and should provide impetus for new interactions.
Combinatorial Group Theory
Author | : Wilhelm Magnus,Abraham Karrass,Donald Solitar |
Publsiher | : Courier Corporation |
Total Pages | : 466 |
Release | : 2004-01-01 |
Genre | : Mathematics |
ISBN | : 9780486438306 |
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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.
Symbolic and Algebraic Computation
Author | : Patrizia Gianni |
Publsiher | : Springer Science & Business Media |
Total Pages | : 564 |
Release | : 1989-08-23 |
Genre | : Computers |
ISBN | : 3540510842 |
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The ISSAC'88 is the thirteenth conference in a sequence of international events started in 1966 thanks to the then established ACM Special Interest Group on Symbolic and Algebraic Manipulation (SIGSAM). For the first time the two annual conferences "International Symposium on Symbolic and Algebraic Computation" (ISSAC) and "International Conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes" (AAECC) have taken place as a Joint Conference in Rome, July 4-8, 1988. Twelve invited papers on subjects of common interest for the two conferences are included in the proceedings and divided between this volume and the preceding volume of Lecture Notes in Computer Science which is devoted to AAECC-6. This book contains contributions on the following topics: Symbolic, Algebraic and Analytical Algorithms, Automatic Theorem Proving, Automatic Programming, Computational Geometry, Problem Representation and Solution, Languages and Systems for Symbolic Computation, Applications to Sciences, Engineering and Education.