  A Garside monoid is a cancellative monoid with a finite lattice generating
set; a Garside group is the group of fractions of a Garside monoid. The family
of Garside groups contains the Artin-Tits groups of spherical type. We
generalise the well-known notion of a parabolic subgroup of an Artin-Tits group
into that of a parabolic subgroup of a Garside group. We also define the more
general notion of a Garside subgroup of a Garside group, which is related to
the notion of LCM-homomorphisms between Artin-Tits groups. We prove that most
of the properties of parabolic subgroups extend to this subgroups.
