BSc Thesis

Algorithmic Problems in Group Theory

King’s College London, 2023–2024
Supervised by Dr David Sheard.

In 1911, Max Dehn introduced the first three decision problems in group theory: the word, conjugacy, and isomorphism problems. This thesis delves into the word and conjugacy problems within finitely presented groups, examining their geometric representations in Cayley graphs and Van Kampen diagrams. It investigates Dehn’s algorithms for the fundamental group of closed orientable surfaces with genus g≥2. Furthermore, it delves into the Novikov-Boone-Britton theorem, which illustrates the undecidability of the word problem for general finitely presented groups.

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