On relative ranks of finite transformation semigroups with restricted range

  • I. Dimitrova South-West University “Neofit Rilski”, Blagoevgrad, Bulgaria https://orcid.org/0000-0002-6078-5968
  • J. Koppitz Institute of Mathematics and Informatics Bulgarian Academy of Sciences, Sofia, Bulgaria
Keywords: transformation semigroups with restricted range, orderpreserving transformations, orientation-preserving transformations, relative rank, relative generating sets


UDC 512.5

We determine the relative rank of the semigroup ${\scr T }(X,Y)$ of all transformations on a finite chain $X$ with restricted range $Y\subseteq X$ modulo the set ${\scr OP }(X,Y)$ of all orientation-preserving transformations in ${\scr T }(X,Y).$ Moreover, we state the relative rank of the semigroup ${\scr OP }(X,Y)$ modulo the set ${\scr O}(X,Y)$ of all order-preserving transformations in ${\scr OP}(X,Y).$ In both cases we characterize the minimal relative generating sets.



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How to Cite
Dimitrova, I., and J. Koppitz. “On Relative Ranks of Finite Transformation Semigroups With Restricted Range”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, no. 5, May 2021, pp. 617 -26, doi:10.37863/umzh.v73i5.288.
Research articles