Permutation Group Algorithms
Permutation Group Algorithms
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USDPermutation 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.
- 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
Product details
March 2003Hardback
9780521661034
274 pages
231 × 157 × 23 mm
0.52kg
30 b/w illus.
Available
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.
