Permutation group algorithms
By: Akos Seress
Series: Cambridge tracts in mathematics -- 152
Publisher: Cambridge University Press
Published: 2003
Place of publication: Cambridge, UK; New York
Language: eng
Number of pages: 264
Subjects: Permutation groups; Algorithms
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.
Notes: Includes bibliographical references (p. 254-261) and index
Table of contents: title: Introduction; title: Black-box groups; title: Permutation groups: a complexity overview; title: Bases and strong generating sets; title: Further low-level algorithms; title: A library of nearly linear-time algorithms; title: Solvable permutation groups; title: Strong generating tests; title: Backtrack methods; title: Large-base groups