Artin groups of extra-large type are biautomatic

Three-generator Artin Groups of Large Type Are Biautomatic

In this article we construct a piecewise Euclidean, non-positively curved 2-complex for the 3-generator Artin groups of large type. As a consequence we show that these groups are biautomatic. A slight modification of the proof shows that many other Artin groups are also biautomatic. The general question (whether all Artin groups are biautomatic) remains open.

conjugacy in relatively extra-large artin groups

in this work we consider conjugacy of elements and parabolic subgroups‎ ‎in details‎, ‎in a new class of artin groups‎, ‎introduced in an earlier work‎, ‎which may contain arbitrary parabolic subgroups‎. ‎in particular‎, ‎we find‎ ‎algorithmically minimal representatives of elements in a conjugacy class‎ ‎and also an algorithm to pass from one minimal representative to the others‎.

Artin groups of euclidean type

Coxeter groups were introduced by Jacques Tits in the 1960s as a natural generalization of the groups generated by reflections which act geometrically (which means properly discontinuously cocompactly by isometries) on spheres and euclidean spaces. And ever since their introduction their basic structure has been reasonably well understood [BB05, Bou02, Dav08]. More precisely, every Coxeter grou...

Artin groups of large type are shortlex automatic with regular geodesics

We prove that any Artin group of large type is shortlex automatic with respect to its standard generating set, and that the set of all geodesic words over the same generating set satisfies the Falsification by FellowTraveller Property (FFTP) and hence is regular.

Rational Subgroups of Biautomatic Groups