2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/166982We use topological methods to study the maximal subgroups of the free idempotent generated semigroup on a biordered set. We use these to give an example of a free idempotent generated semigroup with maximal subgroup isomorphic to the free abelian group of rank 2. This is the first example of a non-free subgroup of a free idempotent generated semigroup.Group Theory20M17;20M05text