  For each group G which decomposes into a finitary direct product of free
groups of finite rank we construct a regular band B such that the free
idempotent generated semigroup over B contains a maximal subgroup isomorphic to
G. In particular, there exists a (regular) band B_0 with the property that any
idempotent generated semigroup whose biordered set is isomorphic to that of B_0
must have all its subgroups abelian.
