A note on free idempotent generated semigroups over the full monoid of partial transformations
Abstract
Recently, Gray and Ruskuc (arXiv:1101.1833) 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 Tn containing e is isomorphic to the symmetric group Sk. We prove that the same holds when Tn is replaced by PTn, the full monoid of partial transformations on 1,...,n.
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