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

Abstract

Recently, Gray and Ru\\v skuc 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 𝒯 n containing e is isomorphic to the symmetric group 𝒮 k . We prove that the same holds when 𝒯 n is replaced by 𝒫𝒯 n , the full monoid of partial transformations on {1,…, n}.