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

Abstract

Let $X$ be an infinite linearly ordered set and let $Y$ be a nonempty subset of $X$. We calculate the relative rank of the semigroup $OP(X,Y)$ of all orientation-preserving transformations on $X$ with restricted range $Y$ modulo the semigroup $O(X,Y)$ of all order-preserving transformations on $X$ with restricted range $Y$. For $Y=X$, we characterize the relative generating sets of minimal size.

References in corpus (4)

• A note on generators of the endomorphism semigroup of an infinite countable chain
• On relative ranks of finite transformation semigroups with restricted range
• On orientation-preserving transformations of a chain
• On Relative Ranks of the Semigroup of Orientation-preserving Transformations on Infinite Chains

Cited by in corpus (1)

• The relative rank of the endomorphism monoid of a finite $G$-set