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Explore advanced algorithms for finitely presented groups in this comprehensive lecture from the Hausdorff Trimester Program on Logic and Algorithms in Group Theory. Delve into computational methods for resolving complex questions about groups defined by finite presentations, including techniques for computing quotients, identifying subgroups of finite index, and generating presentations for these subgroups. Examine the Dehn algorithm in small cancellation and hyperbolic groups, study rewrite systems and the Knuth-Bendix completion algorithm, and investigate automatic structures and their applications. Gain insights into approaches for tackling the conjugacy problem and generalized word problem in finitely presented groups. Build upon fundamental knowledge of group theory to enhance your understanding of these sophisticated algorithmic techniques essential for computational group theory research.
