Permutation Group Algorithms
by Seress, Ákos
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 cent…
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- Full title :Permutation Group Algorithms / Ákos Seress.
Summary
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.
Read More ↓Edition Statements
- Publication Date:2003.
Publication Statements
- Publisher(s):Cambridge University Press
- Place of Publication:Cambridge
- Language:eng
- Publication Date:2003.
The Physical Object
- Description:1 online resource (274 pages)
Edition Identifiers
- ISBN:9780511546549, 0511546548, 9780521661034, 052166103X
- oclc:on1171076516
- LC Classification:QA175
- Dewey Decimal:512/.2
Table of Contents
Introduction -- Black-box groups -- Permutation groups: a complexity overview -- Bases and strong generating sets -- Further low-level algorithms -- A library of nearly linear-time algorithms -- Solvable permutation groups -- Strong generating tests -- Backtrack methods -- Large-base groups.
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