The origins of computation group theory (CGT) date back to the late 19th and early 20th centuries. Since then, the field has flourished, particularly during the past 30 to 40 years, and today it remains a lively and active branch of mathematics. The Handbook of Computational Group Theory offers the first complete treatment of all the fundame

Derek F. Holt, Bettina Eick, Eamonn A. O'Brien

Group Theoretical Preliminaries. History of Computational Group Theory (CGT) and Its Place Within Computational Algebra. Methods of Representing Groups on a Computer. Base and Strong Generating Set Methods in Finite Permutation and Matrix Groups. Coset Enumeration. Computation in Finite Nilpotent and Solvable Groups. Representation Theory, Character Theory, and Cohomology. Algorithms Based on the Normal Structure of Finite Groups. Libraries and Databases of Groups. The Matrix Group Recognition Project. Special Techniques for Computing with Very Large Groups and Their Representations. Quotient Algorithms for Finitely Presented Groups. Rewriting Systems and the Knuth-Bendix Completion Process. Automatic Groups (Methods Involving Finite State Automata)