A note on free idempotent generated semigroups over the full monoid of partial transformations
arXiv:1101.3057 · doi:10.1080/00927872.2011.607875
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 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}.
10 pages; to appear in Communications in Algebra