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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.Read more
- Makes use of the computational group algebra system GAP
- Based on the author's own courses
- Covers very recent developments
Reviews & endorsements
"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
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- Date Published: March 2003
- format: Hardback
- isbn: 9780521661034
- length: 274 pages
- dimensions: 231 x 157 x 23 mm
- weight: 0.52kg
- contains: 30 b/w illus.
- availability: Available
Table of Contents
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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