Permutation Group Algorithms [Seress 2003-03-17].pdf

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Permutation group algorithms comprise one of the workhorses of symbolic
algebra systems computing with groups and play 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 in terms of both asymptotic analysis and 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.
´
Akos Seress is a Professor of Mathematics at The Ohio State University.
CAMBRIDGE TRACTS IN MATHEMATICS
General Editors
´
B. BOLLOBAS, W. FULTON, A. KATOK, F. KIRWAN, P. SARNAK
152
Permutation Group Algorithms
´
Akos Seress
The Ohio State University
Permutation Group
Algorithms

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