  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 be an arbitrary idempotent satisfying |im(e)|=r <
n-1. We prove that the maximal subgroup of the free idempotent generated
semigroup over E containing e is isomorphic to the symmetric group S_r.
