Permutation Group Algorithms [Hardcover]

Theory of permutation group algorithms for graduates and above. Exercises and hints for implementation throughout.Permutation group algorithms 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. Rigorous complexity estimates, implementation hints, and advanced exercises are included throughout. 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.Permutation group algorithms 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. Rigorous complexity estimates, implementation hints, and advanced exercises are included throughout. 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.Permutation group algorithms are indispensable in the proofs of many deep results, including the construction and study of sporadic finite simple groups. This work 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. The book fills a significant gap in the symbolic computation literature for readers interested in using computers in group theory.1. Introduction; 2. Black-box groups; 3. Permutatlóâ