Groupes de Garside

Define a Garside monoid to be a cancellative monoid where right and left lcm's exist and that satisfy additional finiteness assumptions, and a Garside group to be the group of fractions of a Garside monoid. The family of Garside groups contains the braid groups, all spherical Artin-Tits groups, and various generalizations previously considered.² Here we prove that Garside groups are biautomatic, and that being a Garside group is a recursively enumerable property, i.e., there exists an algorithm constructing the (infinite) list of all small Gaussian groups. The latter result relies on an effective, tractable method for recognizing those presentations that define a Garside monoid.