The word problem for Artin groups of FC type Original Research Article

The Artin groups of FC type can be characterized as the smallest class of Artin groups which is closed under free products amalgamated over special subgroups (subgroups generated by a subset of canonical generators) and which contains the finite-type Artin groups. There is a computationally feasible normal form for special cosets of FC-type Artin groups. In particular, the word problem is solvable in quadratic time. It is also shown that FC-type Artin groups are asynchronously automatic and that the set of positive words in a standard presentation of an Artin group of FC type is isomorphic to the monoid given by the same presentation.