  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 groups, and various
generalizations previously considered (In particular, the Garside groups
considered in [1,7] are special cases of those considered here; the latter had
been called "small Gaussian" in earlier works; the name has been changed in
order to uniformize the terminology with works by Bessis, Charney, Michel, and
other authors). 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.
