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, 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.
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.
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
Bibliography
Index