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 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 with other
areas of computer algebra. 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 all 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 of the fundamental algorithms, and
provide detailed worked examples that bring the theorems and
algorithms to life.
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