A Note on Free Idempotent Generated Semigroups over the Full Monoid of Partial Transformations

Abstract

Recently, Gray and Ruškuc proved that if e is a rank k idempotent transformation of the set {1,..., n} to itself and k ≤ n - 2, then the maximal subgroup of the free idempotent generated semigroup over the full transformation monoid In containing e is isomorphic to the symmetric group Lk. We prove that the same holds when In is replaced by PIn, the full monoid of partial transformations on {1,..., n}. © 2013 Copyright Taylor and Francis Group, LLC.