The relations v1 and v2 defined on the lattice ℒ of varieties of inverse semigroups by v1 if and only if and v2 if and only if , where denotes tie variety of groups, are both congruences on ℒ the class v1, is simply the lattice of varieties of grcups and is therefore known to have cardinality .
The class v2 is precisely the sublattice of ℒ consisting of those varieties containing . Each v1-class contains preciselyone element of v2. The main result of this paper establishes that the sublattice v2 of ℒ has breadth . From this it follows that the lattice ℒ/v1 also has breadth . Some consequences concerning varieties generated by fundamental inverse semigroups are also considered.