UBC Theses and Dissertations
Artin groups and local indicability Mulholland, Jamie Thomas
This thesis consists of two parts. The first part (chapters 1 and 2) consists of an introduction to theory of Coxeter groups and Artin groups. This material, for the most part, has been known for over thirty years, however, we do mention some recent developments where appropriate. In the second part (chapters 3-5) we present some new results concerning Artin groups of finite-type. In particular, we compute presentations for the commutator subgroups of the irreducible finite-type Artin groups, generalizing the work of Gorin and Lin [GL69] on the braid groups. Using these presentations we determine the local indicability of the irreducible finite-type Artin groups (except for F₄ which at this time remains undetermined). We end with a discussion of the current state of the right-orderability of the finite-type Artin groups.
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