Maximal subgroups of free idempotent-generated semigroups over the full transformation monoid
Robert M. Gray, Nik Ruškuc · Proceedings of the London Mathematical Society · 2012
Let Tn be the full transformation semigroup of all mappings from the set {1, …, n} to itself under composition. Let E=E(Tn) denote the set of idempotents of Tn and let e∈E be an arbitrary idempotent satisfying |lim (e)|=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 Sr.