Permutation Group Algorithms
Series: Cambridge Tracts in Mathematics; 152;
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Product details:
- Publisher Cambridge University Press
- Date of Publication 17 March 2003
- ISBN 9780521661034
- Binding Hardback
- No. of pages274 pages
- Size 231x157x23 mm
- Weight 520 g
- Language English
- Illustrations 30 b/w illus. 0
Categories
Short description:
Theory of permutation group algorithms for graduates and above. Exercises and hints for implementation throughout.
MoreLong description:
Permutation group algorithms are one of the workhorses of symbolic algebra systems computing with groups. They 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, including 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. A significant part of the permutation group library of the computational group algebra system GAP is based on nearly linear time algorithms. 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.
'The book will be an invaluable tool for anyone who is interested in permutation groups, computational group theory or the broader area of computations involving symmetries and deserves a space on the shelf of any researcher in these areas.' Zentralblatt f&&&252;r Mathematik
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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