Handbook of Computational Group Theory

Praise for the Previous Edition"This is a book I am very happy to have, both for the choice of content and the quality of exposition. Its subject is a very complete and up-to-date review of computational group theory. …All together, the book contains of a huge amount of information. …I think every mathematician will want this book on his shelf." —Mathematics of Computation"It will be an indispensable source for any user in this field."­—G. Kowol, in Monatshefte fur Math, 2007, Vol. 151, No. 3Handbook of Computational Group Theory, Second Edition, offers a complete treatment of all the fundamental methods and algorithms in CGT presented at a level accessible even to advanced undergraduate students. It develops the theory of algorithms in full detail and highlights the connections between the different aspects of CGT and other areas of computer algebra. More advanced and specialized algorithms, particularly those developed more recently, are cited and summarized. While acknowledging the importance of the complexity analysis of CGT algorithms, the authors' primary focus is on algorithms that perform well in practice rather than on those with the best theoretical complexity. Throughout the book, applications of the key topics and algorithms to areas both within and outside of mathematics demonstrate how CGT fits into the wider world of mathematics and science. The authors include detailed pseudocode for all the fundamental algorithms and provide detailed worked examples that bring the theorems and algorithms to life. New to the Second EditionDetailed survey of progress on the matrix groups recognition project, which provides tools for investigating the structure of large groups of matrices over finite fields - it is now possible, for example, to identify quickly the composition and chief factors of groups of this typeDiscussion of a new and effective method of computing character tables of finite groups based on a result of BrauerDescription of new methods for computing the structure of infinite polycyclic groupsSummary of algorithms for studying infinite groups of matrices, including deciding finiteness and the Tits alternative Brief description of new fast methods for solving the word problem in certain types of word-hyperbolic groups, including small cancellation groupsSummary of other significant developments during the past two decades, including a new system for computing in the Monster simple group, which has enabled the construction of its maximal subgroups