Direct products of free groups and free idempotent generated semigroups over bands
arXiv:1109.4402
Abstract
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.
The paper is rendered practically meaningless by arXiv:1301.1225 (accepted for publication in the meantime) since the latter proves a result which is substantially more general, as opposed to the partial, piecemeal result contained in the present note