Maximal subgroups of free idempotent-generated semigroups over the full transformation monoid

Let T-n be the full transformation semigroup of all mappings from the set {1, ..., n} to itself under composition. Let E=E(T-n) denote the set of idempotents of T-n and let e is an element of E be an arbitrary idempotent satisfying vertical bar lim (e)vertical bar=r < n-2. We prove that the maximal subgroup of the free idempotent-generated semigroup over E containing e is isomorphic to the symmetric group S-r.