Group Closures of Injective Order-Preserving Transformations

@article{Catarino2013GroupCO,
  title={Group Closures of Injective Order-Preserving Transformations},
  author={Paula Catarino and Inessa Levi},
  journal={International Journal of Algebra},
  year={2013},
  volume={7},
  pages={703-716}
}
Given a group G of permutations of a finite n-element set Xn and a transformation f of Xn, the G-closuref : Gof f is the semigroup generated by all the conjugates of f by permutations in G. A semigroup S of transformations of Xn is G-normal if GS = G, where GS consists of all the permutations h of Xn such that h −1 fh∈ S for all f ∈ S.W e may assume that Xn is a chain and we let POIn be the semigroup of all the partial and total one-to-one order preserving transformations of Xn. In the present… 

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