TY - JOUR AU - I. Dimitrova AU - J. Koppitz PY - 2021/05/24 Y2 - 2024/03/29 TI - On relative ranks of finite transformation semigroups with restricted range JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 73 IS - 5 SE - Research articles DO - 10.37863/umzh.v73i5.288 UR - https://umj.imath.kiev.ua/index.php/umj/article/view/288 AB - UDC 512.5We 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.  ER -