A note on free idempotent generated semigroups over the full monoid of partial transformations

Details A note on free idempotent generated semigroups over the full monoid of partial transformations A note on free idempotent generated semigroups over the full monoid of partial transformations

2011-01-16

arxiv.org/abs/1101.3057v2

Mathematics

Group Theory

10 pages; to appear in Communications in Algebra

Scientific paper

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}.

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