Permutation group algorithms are indispensable in the proofs of many deep results, including the construction and study of sporadic finite simple groups. This work describes the theory behind permutation group algorithms, up to the most recent developments based on the classification of finite simple groups. Rigorous complexity estimates, implementation hints, and advanced exercises are included throughout. The central theme is the description of nearly linear time algorithms, which are extremely fast both in terms of asymptotic analysis and of practical running time. The book fills a significant gap in the symbolic computation literature for readers interested in using computers in group theory.
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"This book provides a virtually complete state-of-the-art account of algorithms for computing with finite permutation groups. Almost all of the algorithms described are accompanied by complete and detailed correctness proofs and complexity analyses. It is very clearly written throughout, and is likely to become the standard and definitive reference work in the field." Mathematical Reviews
Book Description
Permutation group algorithms played an indispensable role in the proof of many deep results, including the construction and study of sporadic finite simple groups. This book describes the theory behind permutation group algorithms, up to the most recent developments. Rigorous complexity estimates, implementation hints, and advanced exercises are included throughout. The book fills a significant gap in the symbolic computation literature. It is recommended for everyone interested in using computers in group theory, and is suitable for advanced graduate courses.
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Inside This Book
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First Sentence:
Computational group theory (CGT) is a subfield of symbolic algebra; it deals with the design, analysis, and implementation of algorithms for manipulating groups. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
date below level, random subproducts, nonredundant base, base change algorithm, point stabilizer chain, strong generating test, polycyclic generating sequence, block homomorphisms, strong generating set, weighted union rule, permutation group algorithms, labeled branching, product replacement algorithm, nontrivial coordinate, uniformly distributed random elements, constructive recognition, transitive constituent, random prefixes, regular normal subgroups, random conjugates, transversal elements, permutation domain, coset table, backtrack methods, fundamental orbit Key Phrases - Capitalized Phrases (CAPs): (learn more)
Monte Carlo, Las Vegas, Sims's Verify, Proof Let New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Computational group theory (CGT) is a subfield of symbolic algebra; it deals with the design, analysis, and implementation of algorithms for manipulating groups. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
date below level, random subproducts, nonredundant base, base change algorithm, point stabilizer chain, strong generating test, polycyclic generating sequence, block homomorphisms, strong generating set, weighted union rule, permutation group algorithms, labeled branching, product replacement algorithm, nontrivial coordinate, uniformly distributed random elements, constructive recognition, transitive constituent, random prefixes, regular normal subgroups, random conjugates, transversal elements, permutation domain, coset table, backtrack methods, fundamental orbit Key Phrases - Capitalized Phrases (CAPs): (learn more)
Monte Carlo, Las Vegas, Sims's Verify, Proof Let New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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- Computers in Algebra and Number Theory (Siam-Ams Proceedings, V. 4) by G. Birkhoff in Back Matter
- Abstract Algebra: A Computational Approach by Charles C. Sims in Back Matter
- Computation with Finitely Presented Groups (Encyclopedia of Mathematics and its Applications) by Charles C. Sims in Back Matter
- Pure Mathematics: Edexcel Single User Version (Advanced Level Mathematics Tutorials) by Richard Taylor in Back Matter
- An Introduction to the Theory of Groups by Joseph J. Rotman in Back Matter
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- The Lévy Laplacian (Cambridge Tracts in Mathematics) by M. N. Feller in Front Matter
- Quantum Stochastic Processes and Noncommutative Geometry (Cambridge Tracts in Mathematics) by Kalyan B. Sinha in Front Matter
- Linear and Projective Representations of Symmetric Groups (Cambridge Tracts in Mathematics) by Alexander Kleshchev in Front Matter
- Topics in Algebraic Graph Theory (Encyclopedia of Mathematics and its Applications) (v. 1) by Lowell W. Beineke on page 265
- Groups St Andrews 1997 in Bath: Volume 1 (London Mathematical Society Lecture Note Series) (v. 1) by C. M. Campbell on page 63
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