On relative ranks of finite transformation semigroups with restricted range

• Date: 2021
• Main Authors: Dimitrova, I., Koppitz, J., I.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2021
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/288
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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...