Every group is a maximal subgroup of the free idempotent generated semigroup over a band (1301.1225v2)

Abstract: Given an arbitrary group $G$ we construct a semigroup of idempotents (band) $B_G$ with the property that the free idempotent generated semigroup over $B_G$ has a maximal subgroup isomorphic to $G$. If $G$ is finitely presented then $B_G$ is finite. This answers several questions from papers in the area.