Permutation Group Algorithms / Edition 1

Permutation Group Algorithms / Edition 1

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Cambridge University Press

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Permutation Group Algorithms / Edition 1

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.

Product Details

ISBN-13: 9780521661034
Publisher: Cambridge University Press
Publication date: 03/17/2003
Series: Cambridge Tracts in Mathematics Series , #152
Edition description: New Edition
Pages: 274
Product dimensions: 5.98(w) x 9.02(h) x 0.75(d)

Table of Contents

1. Introduction; 2. Black-box groups; 3. Permutation groups: a complexity overview; 4. Bases and strong generating sets; 5. Further low-level algorithms; 6. A library of nearly linear time algorithms; 7. Solvable permutation groups; 8. Strong generating tests; 9. Backtrack methods; 10. Large-base groups.

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