  A number of properties of spherical Artin groups extend to Garside groups,
defined as the groups of fractions of monoids where least common multiples
exist, there is no nontrivial unit, and some additional finiteness conditions
are satisfied \cite{Dgk}. Here we investigate a wider class of groups of
fractions, called {\it thin}, which are those associated with monoids where
minimal common multiples exist, but they are not necessarily unique. Also, we
allow units in the involved monoids. The main results are that all thin groups
of fractions satisfy a quadratic isoperimetric inequality, and that, under some
additional hypotheses, they admit an automatic structure.
