On relative ranks of finite transformation semigroups with restricted range

Abstract

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

References in corpus (1)

• A note on generators of the endomorphism semigroup of an infinite countable chain

Cited by in corpus (1)

• On relative ranks of the semigroup of orientation-preserving transformations on infinite chain with restricted range