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Explore fundamental algorithms for computing in groups defined by finite presentations in this comprehensive lecture from the Hausdorff Trimester Program on Logic and Algorithms in Group Theory. Delve into topics such as computing the largest abelian quotient, identifying subgroups of finite index using Todd-Coxeter coset enumeration, and applying the Reidemeister-Schreier algorithm to compute presentations of subgroups. Examine the Dehn algorithm in small cancellation and hyperbolic groups, study rewrite systems and the Knuth-Bendix completion algorithm, and investigate finite state automata and automatic groups. Learn how to compute automatic structures and apply them to calculate growth rates. Time permitting, gain insights into methods for approaching the conjugacy problem and generalized word problem in finitely presented groups. Enhance your understanding of group theory algorithms through practical examples and applications throughout the lecture.
