| Description |
1 online resource (xiii, 604 pages) : illustrations. |
| Physical Medium |
polychrome |
| Description |
text file |
| Series |
Encyclopedia of mathematics and its applications ; volume 48
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Encyclopedia of mathematics and its applications ; volume 48.
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| Bibliography |
Includes bibliographical references (pages 581-595) and index. |
| Contents |
1. Basic concepts -- 2. Rewriting systems -- 3. Automata and rational languages -- 4. Subgroups of free products of cyclic groups -- 5. Coset enumeration -- 6. The Reidemeister-Schreier procedure -- 7. Generalized automata -- 8. Abelian groups -- 9. Polycyclic groups -- 10. Module bases -- 11. Quotient groups -- Appendix: Implementation issues. |
| Summary |
Research in computational group theory, an active subfield of computational algebra, has emphasized four areas: finite permutation groups, finite solvable groups, matrix representations of finite groups, and finitely presented groups. This book deals with the last of these areas. It is the first text to present the fundamental algorithmic ideas which have been developed to compute with finitely presented groups that are infinite, or at least not obviously finite. |
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The book describes methods for working with elements, subgroups, and quotient groups of a finitely presented group. The author emphasizes the connection with fundamental algorithms from theoretical computer science, particularly the theory of automata and formal languages, from computational number theory, and from computational commutative algebra. The LLL lattice reduction algorithm and various algorithms for Hermite and Smith normal forms are used to study the abelian quotients of a finitely presented group. |
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The work of Baumslag, Cannonito, and Miller on computing nonabelian polycyclic quotients is described as a generalization of Buchberger's Grobner 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. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Group theory -- Data processing.
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Group theory -- Data processing. |
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Group theory. |
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Finite groups -- Data processing.
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Finite groups -- Data processing. |
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Finite groups. |
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Combinatorial group theory -- Data processing.
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Combinatorial group theory -- Data processing. |
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Combinatorial group theory. |
| Genre/Form |
Electronic books.
|
| Other Form: |
Print version: Sims, Charles C. Computation with finitely presented groups 0521432138 (DLC) 92032383 (OCoLC)26672381 |
| ISBN |
9781107088368 (electronic book) |
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1107088364 (electronic book) |
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0521432138 |
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9780521432139 |
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